"Mr. Mondale is the choice of the Wellstone family," said Mike Erlandson, chairman of the state's Democratic-Farmer-Labor Party. Erlandson said Wellstone's son personally asked Mondale on Sunday to take over the race.
A group of up to 875 Minnesota Democrats will meet Wednesday to officially choose the substitute candidate for Wellstone, who died Friday in a plane crash along with his wife, daughter and three campaign workers. Two pilots also died.
The crash threw the battle for control of the Senate into question with the Nov. 5 election nearly a week away. The race had been tight between former St. Paul Mayor Norm Coleman and Wellstone and was a top target of Republicans trying to regain control of the chamber.
Erlandson said the family's choice would weigh heavily in the party's decision. He said he believes Mondale, a household name in Minnesota, will run if nominated.
Mondale, 74, hasn't returned calls to reporters or answered the door at his Minneapolis home.
Those close to Mondale said he isn't expected to comment publicly on a potential candidacy until after Tuesday's memorial service for the crash victims.
If Democrats succeed in drafting Mondale, it will give them a powerhouse candidate for a six-day campaign against Coleman, who entered the race at the urging of President Bush.
State Republican officials have said they would attempt to cast a Mondale-Coleman race as a choice between a reluctant placeholder and someone who is eager to do the work.
Mondale represented Minnesota in the Senate from 1964 to 1976 before becoming vice president under Jimmy Carter. He won the Democratic presidential nomination in 1984 but lost in a landslide to Ronald Reagan.
"Walter Mondale is a good man," Coleman said Sunday, declining to comment further on his potential opponent. "There will be a campaign, but now is not the time."
Erlandson said David Wellstone asked Mondale to run in his father's place. The younger Wellstone and other surviving family members had no comment, the late senator's campaign staff said.
"Mr. Mondale certainly is a very broad sentimental choice of Democrats across the state of Minnesota, but I do remind people that we have a democratic process at the DFL party," Erlandson said.
National Democratic leaders also have reached out to Mondale over the past two days.
During a visit to Wellstone's campaign headquarters Sunday, Senate Majority Leader Tom Daschle said Mondale was clearly the strongest choice, calling him "the great unifier."
"I know Paul would want us to win that election, and we're guaranteed that we're going to do all we can to make that happen a week from Tuesday," Daschle said on CBS's "Face the Nation."
Other names being suggested as possible replacements on the ballot include Mondale's son, Ted, an unsuccessful gubernatorial candidate; Skip Humphrey, former state attorney general and son of former Vice President Hubert Humphrey; state Supreme Court Justice Alan Page, a former pro football star; and state Attorney General Mike Hatch.
White House spokesman Ari Fleischer on Sunday said the administration would wait until the Democrats formally name a replacement before commenting on the race.
"It's still appropriate to let the people of Minnesota grieve," he said.
On Sunday, relatives of the six passengers and two pilots visited the northern Minnesota crash site.
A reconstruction of the flight showed everything appeared normal as the pilot made his approach, Carol Carmody, acting chairwoman of the National Transportation Safety Board said Sunday.
She said they still don't know why the aircraft began drifting south, away from the airport, and slowing down about a minute after the last radio contact.
Carmody said at the time of the crash, pilots reported "light and rime icing" on planes. "Rime" refers to tiny ice crystals. Carmody said Wellstone's plane was equipped with de-icing equipment.
NTSB officials are also looking at the plane's engines for any malfunctions.
The battle for Wellstone's seat was one of a half-dozen or so expected to determine which party will control the Senate next year. The loss of Wellstone leaves the chamber split 49-49 among Republicans and Democrats, with one independent, Jim Jeffords of Vermont, who is allied with the Democrats.
Gov. Jesse Ventura still hasn't decided whether to appoint a temporary successor who would serve until the election winner is officially certified. He met with lawyers Saturday and said if he names someone, it probably will be a Democrat and someone who doesn't plan to run for the office.
It appeared it wouldn't be legal to leave Wellstone's name on the ballot. Absentee ballots already marked for Wellstone won't count for the Senate race, but people who submitted them could go to the polls on Nov. 5 and submit a new ballot.