The Illinois senator told The Early Show national correspondent Tracy Smith that the former vice president would be an "extraordinarily formidable" candidate if he were to join the Democratic fray, adding, "He would have as good a resume as anyone in the field, better — uh — than anybody in the field."
Even so, "I would welcome him to go anywhere he wants to go," Obama remarked.
Speculation about a possible Gore candidacy has been increasing since his. Gore's global warming documentary, "An Inconvenient Truth," earned two statuettes.
On another former White House insider, Obama told Smith he hopes to tone down the rhetoric between himself and fellow presidential contender Sen. Hillary Clinton of New York.
Both are slated to speak in Selma, Ala., on Sunday. But don't expect any heated exchanges like the recent give-and-go between them after Obama backer and Hollywood mogul David. At the time, Obama refused to apologize for Geffen.
But Obama says he wants to take the high road from now on.
"I told my staff that, in those kinds of situations, we should just show some restraint and refrain from some of the snappy comebacks," Obama said.
Did his staff err by responding?
"I think we should have responded," Obama replied, "but in a more restrained way."
This weekend, both Obama and Clinton will head to Selma for a commemoration of the civil rights marches of March 1965.
Obama said the appearance will be personal, not political.
"I think this weekend is actually not about politics. … To me, it represents some of the best moments in American history, where ordinary people stood up to injustice."
Asked if the Selma appearance presents a chance to answer critics who charge Obama hasn't been connected enough to the black community, he replied, "A lot of that has been stuff at the national level. It's not based on the work I've done in Illinois. You don't hear that chatter back home, where I'm well-known."
As Obama gains recognition nationally, he appears to be making inroads. One recent poll shows him winning support from black voters at the expense of Clinton.
On a personal note, Obama told Smith his efforts to give up smoking are working so far, but he knows the pressures of the campaign trial will continue to present challenges to those efforts.