The U.S. Federal Reserve this month asked banks that were part of its stress tests to submit plans to repay government money, if they have not already repaid it, a person familiar with the situation said on Tuesday.

Many U.S. banks are eager to repay money borrowed under the government's $700 billion Troubled Asset Relief Program. Participation in the program comes with limitations on pay, dividend payouts and share repurchases.

Nine banks may soon be allowed to repay money borrowed under TARP, if they have been able to raise common equity recently and if they show they would continue to exceed capital buffers after redemptions, the source said.

In May, the Federal Reserve tested 19 banks to see how well their capital would hold up if the economy deteriorated. Of the 19, 10 were found to need capital. Of those 10, nine have met or exceeded their goals, with the exception of GMAC Financial Services.

Banks that did not need capital according to the stress tests, including JPMorgan Chase & Co and Goldman Sachs Group Inc, repaid TARP funds in June, but a second wave of banks has been agitating to leave the program.

The stress-tested banks that remain in TARP include Bank of America Corp, Citigroup, Fifth Third Bancorp, GMAC, KeyCorp, PNC Financial Services Group, Regions Financial Corp, SunTrust and Wells Fargo & Co.

For Citigroup, leaving the TARP program is a bit more complicated, because the U.S. government owns common shares of the bank as well as trust preferred securities.

The bank has had early conversations with the government about issuing shares to buy back some of the trust preferreds, and also talked to the government about how it might look to sell its common shares, sources said in September.

(Additional reporting by Dan Wilchins in New York and Ajay Kamalakaran in Bangalore; Editing by Andrea Ricci)