The campaign against Yellen has been "tinged with sexist arguments," such as, 'Wouldn't be good in a crisis. Lacks gravitas,'" Bair said in a " Squawk Box " interview, explaining why she feels Yellen is the "best qualified for the job."
(Read More: Obama first to politicize Fed pick: Romney advisor )
"She's got deep experience, very well-respected, great public image. She's not part of the Wall Street club that we've drawn a lot from that group in key financial positions," Bair added.
"The Fed, the Treasury, the OCC [Office of the Comptroller of the Currency], the New York Fed, those are the four top jobs for Wall Street," she explained. "Never have they been headed by a woman."
"This is only about gender to the extent that I think that gender may be one factor if [Yellen] didn't get it," Bair asserted.
Yellen and Larry Summers-Treasury Secretary under Bill Clinton and former director of President Barack Obama's National Economic Council-have emerged in a very public and political fashion as top two candidates to succeed Ben Bernanke as the next Fed chairman.
(Read more: 'Battle-hardened' Summers for Fed head: Altman )
Bair has been critical of Summers, and in a Fortune op-ed last month, she wrote: "Unlike Larry Summers, Tim Geithner , and other Bob Rubin minions frequently mentioned in the financial press as potential Bernanke successors, [Yellen] was not part of the deregulatory cabal that got us into the 2008 financial crisis."
"One of the things that bothers me about Larry is that he's never really said he made any mistakes," Bair explained in Tuesday's CNBC interview. "As far as I know, he's never said that."
In a closed-door meeting with Democratic lawmakers last week, Obama is said to have told the group that he's interviewed several possible nominees, mentioning Yellen, Summers, and former Fed Vice Chair Don Kohn by name.
"I think Don is very solid. He does know monetary policy. He's been at the Fed for years. He's loved by the Fed staff. He's well-respected on the Hill. He's a good quality guy," Bair acknowledged, "but Janet should get the job. She's best qualified."
Bernanke is not expected to serve for a third time as Fed chairman when his current four-year term expires in January.
Back in June, it was the president who jumped-started the conservation about Bernanke's possible departure by hinting in a Charlie Rose interview that the Fed chief may be on his way out.
"Nobody understands why [Obama] did that," Bair said, explaining that she generally agrees with Bernanke and Yellen on monetary policy, which has been on an unconventional track including the current $85-billion-a-month bond-buying program and near-zero interest rates.
(Read more: No Fed taper before year-end, strategist says )
Talk about the changing of the guard at the Fed comes at a time when investors are wondering when the central bank may start to taper those massive bond purchases-a move many on Wall Street believe could happen as soon as next month.
Bair said that Bernanke and by extension Yellen started these extraordinary policies so "maybe they're best equipped to get us out of it."