The chairman of the Senate Banking Committee on Tuesday hedged when asked whether or not he would back Elizabeth WarrenElizabeth Ann WarrenOvernight Finance: Lawmakers grill Equifax chief over hack | Wells Fargo CEO defends bank's progress | Trump jokes Puerto Rico threw budget 'out of whack' | Mortgage tax fight tests industry clout Michelle Obama is exactly who the Democrats need to win big in 2020 Wells Fargo chief defends bank's progress in tense Senate hearing MORE to head the newly-created Consumer Financial Protection Agency (CFPA).

"If the president wants to name her and it goes through the hearing process, then fine, she'll have my support," Sen. Chris Dodd (D-Conn.) told the Hartford Courant editorial board. "But she has to tell me more than just she's a good consumer advocate or that's she's got a great campaign.

"It isn't just a question of being a consumer advocate. I want to see that she can manage something, too."

Warren, a Harvard Law School professor who chaired the panel that scrutinized the federal bailout of financial institutions, is a leading candidate for the position. Liberal political groups have pressed the White House to nominate her. 

Speculation has ramped up in recent days that Warren could be named to the position. Last Thursday, she met with White House senior advisers David Axelrod and Valerie Jarrett about her potential nomination, but no decision was made. 

The Washington Post reported Wednesday that before that meeting, Warren met with the Financial Services Roundtable, an influential group of banking lobbyists. 

The consumer protection agency was created by the Wall Street reform legislation that Dodd shepherded through the Senate. 

Dodd on Tuesday questioned whether Warren could garner enough support in the Senate to win the 60 votes necessary to be confirmed. 

"My simple question about Elizabeth is: Is she confirmable?" Dodd said. 

In previous comments, Dodd said that Warren "would be a terrific nominee."