(CNN) -- Several close friends and supporters of Sen. Hillary Clinton said they are seeking a "graceful exit strategy" for Clinton from the race for the Democratic nomination, possibly as part of a joint ticket for the White House.
Sources say Clinton insiders are discussing an exit strategy for the New York senator.
The discussions are not taking place between the campaigns but rather among informal campaign advisers on both sides who are trying to actively influence and shape the debate as the competition nears a close June 3.
Bill Burton, national spokesman for Obama's campaign, said that "there are no talks under way between the campaigns" and that any suggestion from Clinton insiders is "unequivocally untrue."
"We are two campaigns, in real competition, not having any such talks about exit strategies," Burton said.
Obama campaign chief strategist David Axelrod said "there have been zero discussions, back-channel or otherwise, between the campaigns."
Clinton campaign aides also deny that any talks are taking place between the campaigns, emphasizing that the contest is not over. Clinton herself said the report was "flatly untrue" during a meeting with the editorial board of a South Dakota paper Friday.
But some Clinton camp insiders and close friends are actively floating three scenarios that they believe will influence whether or how the two teams merge.
The first scenario is if Obama ignores Clinton and her supporters and makes the vice presidential offer to someone else.
One insider said, "This would be a total dismissal of her and totally unacceptable."
"This could mean open civil war within the party," another said. "A rupture in the party. If he doesn't offer at all, you've got a breakdown. A real resentment there."
Another source said it would not mean Clinton would refuse to campaign for Obama. But she would do so the way President Clinton campaigned for Al Gore, which the source characterized as "aloof."
Another source said it would affect the willingness of some women's groups to raise money for Obama.
The second scenario they foresee is for Obama to publicly offer Clinton the vice presidential spot, with the understanding that she would turn it down. But several Clinton friends say "the problem is, the two sides do not trust each other" to follow through on this.
The third scenario they envision would be trying to get both the candidates to sit down face-to-face and work out an agreement suitable to both parties. Some Clinton insiders say some points to consider would be how to help pay off the Clinton campaign debt -- roughly $30 million -- or whether he would offer support for a possible Clinton effort to become Senate majority leader.
Clinton insiders say Hillary Clinton is aware that some of her supporters are pushing for her to get an offer to join the ticket, but they say she has not thought about whether she wants the vice presidential slot because she's still campaigning for the top job.
There is a real split in the Clinton camp over whether she should even accept an offer to join the ticket, if it were to materialize.
On Thursday, meanwhile, a veteran Democratic activist said former Fannie Mae CEO Jim Johnson has accepted Obama's request to begin a screening and selection process for the No. 2 spot. Watch what will influence Obama's choice for VP »
Johnson performed a similar role for Democratic presidential nominees Walter Mondale in 1984 and John Kerry in 2004.
Obama campaign spokesman Bill Burton declined to comment on the report of his candidate's running mate search. But sources inside the Obama campaign say the top considerations for the job are likely to be age -- Obama is only 46 -- and national security experience.
Among possibilities mentioned by Obama insiders are former Sen. Sam Nunn of Georgia, retired Gen. Wesley Clark and former Democratic presidential rival Sen. Joe Biden.
Obama has publicly deferred questions about whether he would consider Clinton for the No. 2 spot, saying it would be presumptuous to talk about running mates before he has the nomination sewn up.
But he acknowledges what Clinton would bring to a ticket.
"Sen. Clinton has shown herself to be an extraordinary candidate," he said. "She is tireless; she is smart. She is capable. And so obviously, she'd be on anybody's short list to be a potential vice presidential candidate."
Democrats also speculate that Obama could pick a major Clinton backer, such as Indiana Sen. Evan Bayh, Ohio Gov. Ted Strickland or Pennsylvania Gov. Ed Rendell, who could deliver key swing states.
Another possibility could be one-time rival John Edwards, the former North Carolina senator who endorsed Obama last week. Edwards, who was John Kerry's running mate in 2004, says he's not interested.
Other possibilities include New Mexico Gov. Bill Richardson, another former presidential rival whose résumé is long on foreign policy experience and who would appeal to Latino voters, and Kansas Gov. Kathleen Sebelius, a rising star in the party who would help with the women's vote.
Obama said Thursday that he is not discussing his selection process and does not have criteria for a running mate.
"No criteria right now. I still have to win the nomination," he said.
Although Obama is the Democratic front-runner and has captured a majority of pledged delegates after Tuesday's Kentucky and Oregon primaries, he has not clinched the 2,025 delegates needed to win the nomination against Sen. Hillary Clinton.
Despite the math, Clinton has vowed to remain in the race.