Rep. Kendrick Meek went on national morning TV news shows to swat down reports that he had told Clinton, who was campaigning for Meek, that he would drop out to improve Crist's chances of defeating the front-runner, Republican Marco Rubio. Crist left the GOP to run as an independent after Rubio led him before the Republican primary.
Meek said it was Crist who had suggested the idea to Meek. He said Crist had also called Clinton's office "trying to persuade them to get me out of this race."
"Gov. Crist talked to me about getting out of the race. I recommended to the governor that he should consider getting out of the race," Meek said on CNN's "American Morning."
Crist's spokesman did not immediately respond to e-mails seeking comment.
Meek said he had talked with Clinton about the idea while the president was campaigning for Meek. He said Clinton privately asked him about rumors that he would quit the campaign.
"I told him I didn't have any thoughts about getting out of the race. He didn't encourage me to get out of the race," Meek said on ABC's "Good Morning America".
Polls indicate Meek has little chance of winning on Tuesday, badly trailing Crist and Rubio. The idea of Meek quitting so voters in his camp would kick their support to the more moderate Crist, instead of the conservative Rubio, has been swirling around the campaigns for some time.
Meek on Thursday said a report by Politico that was confirmed by a Clinton spokesman "was inaccurate at best" that the former president while campaigning in Florida last week asked him to withdraw.
Clinton acknowledged during an interview aired on CNN's Anderson Cooper 360 that Meek wanted to discuss the possibility of withdrawing, so they did. He did not say he asked Meek to quit.
"I said in the end, you know, he would have to do what he thought was right. He'd have to do what he felt right about," Clinton said.
As for the specifics of the conversation, Clinton said that would have to stay between the two men, who have been friends for years.
Meek said Friday that idea "seems to be a part of the Crist strategy for me to sell out on the state of Florida."
"I'm not in that business, I'm not going to do it, I haven't done it," Meek said.
Democratic Party Chairman Tim Kaine, appearing on CBS's "The Early Show," said he has heard nothing about any discussion between Clinton and Meek about Meek withdrawing from the race. He said the party has invested heavily in the Florida race and is putting it's muscle behind Meek.
"In a three-way race that's still volatile, I think he's got an excellent chance," Kaine said about Meek.
Experts say Crist would need the Democrats backing Meek to have any shot at winning.
"Charlie Crist truly will say and do anything to get elected and hold on to power," Rubio senior strategist Todd Harris said in a statement. "Secret deals to trade away principles for power is already the problem in Washington, it's not the solution. This is simply politics as usual which is exactly what voters across the country are emphatically rejecting this election."
Clinton has been campaigning all over the country, trying to keep the U.S. House and Senate in Democrats' hands. Meek said Clinton has done 11 events for his campaign.
During primary season, the White House was embarrassed when it became known that it enlisted Clinton to try to ease Rep. Joe Sestak out of Pennsylvania's Senate primary with a job offer. The White House released a report describing the offer that was intended to clear a path for Sen. Arlen Specter to win the Democratic nomination.
Sestak beat Specter and Clinton was campaigning for him Thursday.
Republicans instantly sought to gain from the episode surrounding Meek.
"One can only imagine the response if Republican leadership tried to force out of the race - in the 11th hour - a qualified black candidate like Kendrick Meek," RNC Chairman Michael Steele said in a statement.
Clinton downplayed that, saying of course the Republicans want Rubio to win.
Robert F. Kennedy Jr. earlier this month said that Meek cannot win the race and instead endorsed Crist. He called the Florida Senate race the most critical in the country and urged voters to combat what he calls the radical tea party movement by voting for Crist.
Crist's camp said the Politico report was accurate, and that Crist "is the one candidate who can defeat tea party extremist Marco Rubio and deliver bipartisan results for Florida in Washington."
Many Florida voters have already cast early and absentee ballots, so even if Meek dropped out it might have only a marginal effect. His name also would remain on the Election Day ballot.
Meek said he saw no advantage to withdrawing.
"There's no negotiation about me getting out of the race - that's the bottom line."
Brendan Farrington in Tallahassee and Liz Sidoti in Washington contributed to this report.