The requests are pending, and no decision has been made on whether the investment banks will get approval to repay the money and sever ties with the Troubled Asset Relief Program, according to two people familiar with the matter.
They spoke on condition of anonymity because the banks' discussions with the Fed are ongoing.
Goldman Sachs, Morgan Stanley and JPMorgan Chase & Co. have said for weeks that they want to repay their share of the $700 billion government bailout so they can operate free of federal limits on executive pay and other restrictions.
A JPMorgan spokesman declined to comment on whether the bank also has requested permission to repay TARP. Goldman Sachs and Morgan Stanley representatives also declined to comment.
The Federal Reserve, the main regulator for all three banks, would have to approve any decision on repaying bailout funds.
Goldman and Morgan, which each received $10 billion under TARP, initiated talks with the Fed in the past few weeks, according to the people. The banks were among nine large financial institutions that took an initial $125 billion in bailout money in October after the collapse of Lehman Brothers threatened to trigger a financial catastrophe.
If their requests are approved, Goldman and Morgan would be the first among the nine banks to repay bailout money. Twelve smaller banks have returned nearly $1.2 billion in government money so far. More than 570 banks have received about $198 billion in TARP funds.
Banks that want to repay bailout money must be able to replace the funds by raising capital without guarantees from the Federal Deposit Insurance Corp.
The issue of repaying TARP money is a sensitive one for the government. By allowing strong banks to abandon the bailout and its restrictions, it risks putting weaker banks at a disadvantage, analysts say. A big concern is that high-level employees of bailed-out banks could defect to rivals that have paid back the funds.
"Paying back TARP money would clearly be seen as a sign of strength," said Douglas Elliott, fellow at Brookings Institute and former investment banker at JPMorgan. "It would be much easier for a Goldman Sachs to hire someone from another bank if it's not bound by TARP restrictions."
The Treasury Department declined to comment Monday on whether Goldman or Morgan had applied to repay bailout money.
Treasury has said it expects banks to repay $25 billion in government funds over the next year. The Obama administration said earlier this month that the repaid funds would be used for further injections into banks.
The government "stress tests" on the nation's 19 largest banks found that 10, including Bank of America Corp. and Citigroup Inc., needed to raise additional capital to survive a worsening recession.
Goldman Sachs and JPMorgan were among the nine banks found to have enough capital.
Morgan Stanley needs an extra $1.8 billion in capital, the stress tests ruled. The bank has already begun raising the money through stock offerings.