The maneuver may also be aimed at countering an image in voters' minds of Obama as presidential material and at helping restore an aura of inevitability as the party's nominee that Clinton had early in the campaign but lost.
"The Clintons are in a difficult position," said Dennis Goldford, a political science professor at Drake University in Iowa, who has tracked the presidential race.
"If she wins the Democratic presidential nomination, she would need Obama's supporters. But she needs to be careful. If this talk of him on the ticket is seen as a cynical maneuver, it could backfire and hurt her," Goldford said.
Former Senate Democratic leader Tom Daschle of South Dakota, an Obama backer, mocked the idea.
"It may be the first time in history that the person who is running number two would offer the person running number one the number two position," Daschle told "Meet the Press".
Obama leads Clinton, a fellow Democratic senator, in a bruising race for their party's presidential nomination, but neither is likely to reach the 2,025 delegates needed to become the nominee in the remaining state-by-state contests.
As Democratic leaders worry about the damage that could be done if neither has a clear lead by the August nominating convention, the party is also trying to decide what to do about election results from Michigan and Florida that do not count because of a dispute over when they were held.
The Clintons have charged that Obama, a charismatic lawmaker from Illinois, lacks the experience to handle an international crisis as president.
But since Clinton, a two-term senator from New York, won primary elections in Ohio and Texas, she and her husband, former President Bill Clinton, have touted Obama as a possible running mate.
When asked about the possibility last week, Obama said he was focused on winning the nomination. "I think it is very premature to start talking about a joint ticket," Obama said.
