CBS News Chief White House Correspondent John Roberts reports the North Carolina Democrat gave nothing away to the media.
"I'm going to stay with my policy of not talking about this. So, I'm just continuing to do my job," Edwards said.
The current speculation is that Edwards is on a "short list" with three other senators: Evan Bayh of Indiana, John Kerry of Massachusetts and Joe Lieberman of Connecticut.
But it's hard to predict if Gore will stick to that list.
He told reporters Thursday that, "It's down to sixwith one wild card."
The could include the four senators plus New Hampshire Gov. Jeanne Shaheen and House Minority Leader Dick Gephardt, D-Mo.
Both Shaheen and Gephardt have all but removed themselves from contention, but sources say Gore may still reach out to the Missouri congressman, a favorite of labor unions who is identified with the party's progressive wing.
As for the "wild card," it could be former Treasury Secretary Robert Rubin.
With his pick of a running mate, Gore says he's looking for "Someone who can become president if necessary. Someone who can be a good partner. Someone who shares my values and will fight for the people, not the powerful."
Gore also might be looking to lock up a key state with his pick, project a youthful image to contrast with the Republican ticket or send a message about his campaign.
"People are going to have a choice," said Gore campaign press secretary Chris LeHane. "Do they want to turn the clock back and go and return to the Bush, Quayle, Cheney years, or do they want to move forward?"
Youth is definitely in Edwards' favor. The baby-faced, 47-year-old former trial lawyer is a rising star in the Senate.
Gore insiders say his image as an eloquent family man with a lifetime record of fighting for people is just what they are looking for.
Edwards' only drawback could be his freshman status in the Senate. He has been in politics only 2 years.
But Gore has told CBS News, "I don't think that experience in Washington is the only kind of experience that matters."
Still, Edwards isn't the only name still in contention.
Kerry, who returned to Washington from Idaho Saturday, is a decorated Vietnam veteran and still high on the list.
"If you are trying to send a message you might think about John Kerry," said Democratic pollster Mark Mellman. "You put two Vietnam veterans on the Democratic ticket against a Republican ticket where both parties on the ticket chose not to serve."
Connecticut's Lieberman, on the other hand, was noted for his criticism of President Clinton during the impeachment scandal and could inoculate Gore against attacks on moral issues.
Gore also hopes to avoid the potshots he Bush campaign took over George W.'s pick of Dick Cheney for his running mate.
Cheney's voting recordwhich included a "nay" vote on a resolution calling for Nelson Mandela's release from a South African jailcaused a stir that the Gore campaign quickly tried to capitalize on.
Here's a look at the extended list of Democratic could-bes and wannabes:
The Four Tops?color>
First-term senator from Indiana, 44. Elected governor of Indiana in 1989, and served until his election to the Senate in 1998. Son of former Indiana senator and 1976 Democratic presidential candidate Birch Bayh.
Pro: A safe and solid choice. An up-and-comer in the Senate. A former Governor from a state that usually votes Republican.
Con: Not much help geographically, from a solidly Republican state. Considered too much of a Gore clone. His vote to ban late term abortion has angered women's groups.
A 47-year-old freshman senator from North Carolina. He won a tough race against the GOP incumbent in 1998. Was impressive during Clinton impeachment hearings.
Pro: Youthful, dynamic politician who could provide a favorable contrast to Dick Cheney. Senior senators will tout him as a once-in-a-generation whiz kid who can't be passed up.
Con: Republicans would have fun with the fact that Edwards was a wealthy trial lawyer. He has been in politics only two years.
Third-term U.S. senator from Massachusetts, 56. Top Democrat on the Senate Small Business Committee. Received a Silver Star, a Bronze Star and three Purple Hearts for service in Vietnam. Former prosecutor and lieutenant governor of Massachusetts.
Pro: War hero. Strong credentials on foreign policy, crime-fighting and the environment. Tough campaigner.
Con: A liberal from a state Gore's already likely to win, who, like Gore, angered unions with support for NAFTA.
U.S. senator from Connecticut, 58. Chairman of the Democratic Leadership Council since 1995. Bill Clinton, then a Yale Law School student, campaigned for Lieberman during his bid for a State Senate seat. Castigated Mr. Clinton over the Monica Lewinsky scandal.
Pro: Moderate. Would be first Jew on a national ticket. Viewed as a straight shooter and a person who cares about moral values.
Con: Somewhat lackluster. Is an observant orthodox Jew, which could make him somewhat controversial.
The Rest Of The Pack color>
Former three-term senator from New Jersey, 56. Ended his bid for the presidency in March. Hall-of-fame basketball player for the New York Knicks. Has 340 primary delegates, who he has refused so far to release.
Pro: Would help Gore gain credibility on campaign finance reform. National name recognition. Could help lure Independents.
Con: Still bad blood between him and Gore. Some of his attacks on Gore might gain prominence. Says he's not interested in job.
William S. Cohen
Secretary of Defense, 59. Former three-term Republican senator from Maine. Also served three terms in the House of Representatives. Co-authored a novel with former Colorado Senator Gary Hart.
Pro: Could give the ticket bipartisan appeal. Has international stature.
Con: From a small state. Said in April that he's probably going to vote for Bush. Some view him as a lightweight.
Andrew M. Cuomo
Secretary of Housing and Urban Development, 42. Son of three-term New York Governor Mario Cuomo. Married to Kerry Kennedy, the 7th child of the late Sen. Robert F. Kennedy.
Pro: From a key electoral state. Some starpower because of his father and wife. Very popular with liberals.
Con: Never elected to office. Untested as a candidate. Record as an administrator has been questioned.
Senate Minority Leader, 52. U.S. senator since 1987. Served in the House of Representatives from 1978-1986.
Pro: Has some national visibility, good fund-raiser, well-versed on the issues. Close to former Gore campaign manager Tony Coelho.
Con: From a small state. Has had some bad press over favoritism to friends in the cell phone and airline business.
Governor of California, 57. Elected lieutenant governor in 1994 under Republican Gov. Pete Wilson.
Pro: From the largest state in the nation. Hallmark of his policy agenda is education. Proven appeal to Hispanics. Catholic.
Con: Gore is already popular in California. Lacks charisma.
U.S. senator from Illinois, 55. Served in the House of Representatives from 1982-1996. Former professor at Southern Illinois School of Medicine.
Pro: Ranked as a rising star in the Senate. Illinois is a swing state and his regional ties might help in battleground states of Michigan and Ohio. Catholic.
Con: Lacks national name recognition. One of President Clinton's most outspoken supporters during the Monica Lewinsky incident.
U.S. senator from California, 66. First woman ever to serve on the Senate Judiciary Committee. Ran unsuccessfully for governor against Republican Pete Wilson. Former mayor of San Francisco.
Pro: A woman with significant executive experience.
Con: Gore is already popular in California. She is in a competitive re-election race against Republican Tom Campbell and would have to give up her Senate seat to run. Democrats could lose the seat if she drops out.
U.S. senator from Florida, 63. Former governor of Florida. Served in the Florida State Senate from 1970-1978, and in the Florida House of Representative from 1966-1970.
Pro: Moderate. Could help Gore compete in Florida; popular with Cuban-American community. Few enemies. Reputation as a meticulous campaigner.
Con: Lacks charisma. Kept potentially embarrassing minute-by-minute diaries of his daily life.
U.S. senator from Nebraska, 56. Governor from 1982 to 1987. Former Navy SEAL and Congressional Medal of Honor recipient. Injured in Vietnam War. Ran a bitter campaign for president against Bill Clinton in 1992. Announced in January he would not seek re-election to the Senate.
Pro: Appeal among Independents. War hero. Colorful.
Con: Supported Bradley in primary. Many Democrats don't view him as a team player. Has just accepted a new job in the private sector.
Former U.S. Senate majority leader, 66. Served as chief negotiator during Northern Ireland peace process. Former U.S. District Judge and U.S. Attorney from Maine.
Pro: Significant experience in both domestic and foreign policy. A strong campaigner.
Con: Out of public office. Viewed as very partisan by Republicans.
Former U.S. senator from Georgia, 62. Served as chairman of the Senate Armed Services Committee. Currently co-chairman of the Concord Coalition, a nonpartisan group dedicated to eliminating federal budget deficits and strengthening social security.
Pro: Could appeal to moderates and independents. Strong credentials on defense. Well-respected on Capitol Hill. Works well with Republicans.
Con: Independent minded. Doesn't always tow Democratic Party line. Out of public life for past four years. From same region as Vice President Gore.
Franklin D. Raines
Chairman and CEO of Fannie Mae, 51. Former director of the Office of Management and Budget.
Pro: African American. His leadership helped balance the budget. Expert on financial matters and domestic policy.
Con: Untested candidate. Never elected to public office.
Chairman of the executive committee, Citigroup Corp., 61. Former Secretary of the Treasury in Clinton administration. Spent 26 years at Goldman Sachs & Co.
Pro: It's the economy, stupid. Would be first Jewish candidate on major party ticket.
Con: Has never run for office. Said to prefer being head of the Fed when Alan Greenspan leaves.
Popular New Hampshire governor played a key role in Gore's Granite State primary victory.
Pro: A skillful politician adept a dealing with New Hampshire's arch conservatives. Well known in th party and trusted.
Con: She has no interest in becoming vice president.
Kathleen Kennedy Townsend
Maryland's first female lieutenant governor, 48. Served as a Deputy Assistant Attorney General, U.S. Department of Justice, from 1993-1994. Eldest child of the late Robert F. Kennedy.
Pro: Female. Viewed as an up-and-comer within the Democratic Party. A Kennedy.
Con: Highest office she's held is lieutenant governor. Said to be positioning herself to run for governor. A Kennedy.