The wooing of Tim Geithner has begun.

The former Treasury Secretary, who stepped down in January and sealed a book deal with Random House earlier this month, has been fielding calls from at least one major financial firm about a possible future job, the FOX Business Network has learned.

Geithner has recently held a series of meetings with BlackRock (BLK) chief executive Laurence Fink, according to three people with direct knowledge of the matter. Although no specific job at the big money management firm has been discussed, Fink and Geithner discussed possible future employment, these people say.

Geithner is currently a distinguished fellow at the Council on Foreign Relations; he has told people he plans to remain at the council and write his book at least for most of the next year.

But after that, Geithner has told people he’s keeping his options open, including taking a job in the private sector.

When Geithner announced he stepping down as Treasury Secretary last year, speculation swirled that he would join a big bank, like Citigroup (C). “If he was the chairman of Citigroup, he would be a dynamic person who would enhance the bank’s stature,” influential analyst Dick Bove told FOX Business at the time.

Fink, the same people say, is making an early pitch for Geithner to join BlackRock even if the recent conversations between the two men didn’t result in a formal job offer, or according to one person, a discussion of any specific role Geithner might play at BlackRock.

That said, Geithner could be a valuable addition at the world’s largest money management firm. BlackRock has feasted off of government contracts, including managing the toxic assets assumed by the Federal Reserve following the banking crisis. Geithner could be a valuable ambassador in dealing with the Obama Administration and the Federal Reserve, given his experience as president of the New York Fed, the chief regulator of the U.S. financial system.

"Larry has made no secret how much he thinks of Tim," said one person who knows both men, who described the talks as "wide-ranging discussions" about Geithner's future in a possible private sector job, including at BlackRock. A spokesman for BlackRock, Jim Badenhausen, declined to comment; Jenni LeCompte, a spokeswoman for Geithner, also declined to comment.

As first reported by the FOX Business Network, Geithner’s book is expected to offer an inside look at the 2008 financial crisis when he was New York Federal Reserve president and his role as President Obama’s first Treasury secretary for most of the rest of the year.

Geithner was one of the architects behind the controversial bailouts of Bear Stearns, American International Group (AIG) and the grand bailout of the banking system known as the Troubled Asset Relief Program, or TARP. He also played a role in the decision to let investment bank Lehman Brothers fail, which sent shockwaves through world markets.

Geithner has spent the vast majority of his career is various government positions including Under Treasury Secretary of Treasury during the Clinton Administration. He is a close associate of former Clinton Treasury Secretary Robert Rubin, a co-chairman of the Council on Foreign Relations.

Rubin served as a senior executive of Citigroup but resigned in 2009 amid criticism over his role in the   firm’s risk taking that led to a massive government bailout orchestrated by Geithner, then Treasury Secretary Hank Paulson and Federal Reserve chief Ben Bernanke.

But people who know Geithner say he’s also leaving his options open for a possible role in government, such as replacing Bernanke as Federal Reserve chairman.

Fink, meanwhile, has told people that he wants to bring Geithner to BlackRock, even if Fink has also expressed a desire to take Geithner's old job as Treasury Secretary, which recently went to Jack Lew.

“Getting the former Treasury Secretary to join BlackRock would be the next best thing for Larry,” said one senior Wall Street executive who asked not to be named.

Matt Egan contributed to this report.

Charles Gasparino joined FOX Business Network (FBN) in February 2010 as Senior Correspondent.