Rep. Debbie Wasserman Schultz (D-Fla.) is one of the names in the mix to head the Democratic National Committee should Chairman Tim Kaine run for Senate next year, but she isn't revealing whether she has any interest in the post. 

"I understand there is a DNC chairman at the moment," Wasserman Schultz said Tuesday when asked about top Democrats dropping her name as a contender to head the committee. 

Asked if she would have any interest in the slot should Kaine officially jump into the race for retiring Sen. Jim Webb's (D-Va.) seat, Wasserman Schultz simply repeated her earlier dodge.     

While Democratic insiders put her name near the top of the list of possibilities to head the DNC, working against Wasserman Schultz is her role at the Democratic Congressional Campaign Committee. 

The Florida congresswoman is one of five DCCC national chairmen for the 2012 cycle and is working on the committee's redistricting efforts. That role would present an inherent conflict, said one Democratic insider, given that the two committees compete for donors. 

Other names at the top of the list are former Ohio Gov. Ted Strickland and former Michigan Gov. Jennifer Granholm, both of whom are pegged as more likely to be selected for the DNC job than Wasserman Schultz. 

One thing tying all three together — they were all supporters of then-Sen. Hillary Rodham Clinton's (D-N.Y.) 2008 presidential campaign.

Earlier this week, a DNC spokesman said Kaine is "increasingly likely" to jump into the 2012 Senate race, making an official announcement more a question of when than if at this point.