Yellen received strong support from Democrats with 11 of 12 on the panel approving her nomination and partial support from Republican with three of 10 voting to send her nomination to the full Senate for confirmation, The Wall Street Journal reported.
Senate Democrats also pushed a rule change Thursday that will limit the use of filibusters opposition parties have used to slow or derail presidential nominations.
At this point, at least six Republican senators have indicated they would support Yellen's nomination, including the three on the banking panel. With 55 Democrats likely to provide strong support, Yellen's confirmation in the Senate is close to guaranteed, the Journal said.
"She is extraordinarily well-qualified. I think she comes to the Fed with really some of the best credentials we've ever seen for someone to head up the Fed," said banking committee member Sen. Elizabeth Warren, D-Mass.
From the other side of the aisle, "I start from the position of wanting to give the president whoever he picks. So naturally I am leaning in that direction. I think highly of her," Sen. Orrin Hatch, R-Utah, said Thursday.
Yellen has been the Fed's vice chairwoman since 2010.
Outgoing Chairman Ben Bernanke, whose second term as head of the Fed ends Jan. 31, has also voiced approval of his successor.
"I agree with the sentiment, expressed by my colleague Janet Yellen at her testimony last week, that the surest path to a more normal approach to monetary policy is to do all we can today to promote a more robust recovery," Bernanke said in a speech this week.