The Huffington Post has an intriguing report this morning which says that U.S. Sen. Claire McCaskill, D-Mo., is the front runner to be the new chairman of the Democratic National Committee.

She would replace former Vermont Gov. Howard Dean, who is stepping down in January.

According to the report, the plan would call for McCaskill to be the public face of the party, but for Democratic president-elect Barack Obama’s deputy campaign manager, Steve Hildebrand, to be the “operational chair” (in other words, handle the day-to-day stuff).

UPDATE, 4:30 p.m.:

McCaskill spokeswoman Maria Speiser played down the speculation. “It’s all just a rumor. We’re not sure who started it,” Speiser said. “Claire has not had any conversation with the Obama team about the position, or with the president-elect Obama himself.”

Speiser emphasized that McCaskill earlier has made it clear, even before the election, that she had no plans to quit her Senate seat for a Cabinet position. “She’s pretty happy being a senator and representing Missouri,” Speiser said.