Regulators' plans for bailing out the floundering Federal Savings and Loan Insurance Corp. have run into opposition from the White House, which is working on a plan of its own to rescue FSLIC, administration and industry sources said this week.

The formation of an S&L to take over and dispose of $3.1 billion in real estate and other assets that the insurance corporation has taken over from failed savings and loans was announced three weeks ago by Edwin J. Gray, chairman of the Federal Home Loan Bank Board, which regulates the thrift industry and FSLIC. The new institution is known as the Federal Asset Disposition Association (FADA).

Federal funds, derived from the home loan banks in the form of borrowings by FADA, probably would finance the new association, a plan that goes against the grain of the Reagan administration. The White House wants a plan that would have most of the rescue work done by private industry, sources said.

This may not be easy, according to an industry leader. "I don't know of a way of disposing of a bad asset without someone taking a loss, so the idea of privatizing losses bemuses me. Somebody has to pay," said David O. Maxwell, chairman of the Federal National Mortgage Association, which buys residential mortgages and sells the loans or securities backed by pools of loans on the secondary market.

A working group composed of officials from the Treasury and Justice departments, the Office of Management and Budget and the Council of Economic Advisers is trying to put together its own plan, according to sources. Another option, prohibiting FSLIC from using federal money to fund FADA, also is being discussed, the sources said.

"We don't discuss" the actions of a working group until it makes recommendations to the White House, a Treasury spokesman said.

The White House's failure to decide on an administration policy regarding FSLIC's troubles has angered Rep. Fernand J. St Germain (D-R.I.), chairman of the House Banking, Finance and Urban Affairs Committee.

"I think it is time for the president to get involved" if the administration agrees that major problems exist in the financial industry, St Germain said last month during hearings of the financial institutions subcommittee of the Banking Committee. "Congress should not be expected to be the entire cleanup crew." He also said Congress will not pass legislation until it has "a clear picture of administration policy, including what happens to FSLIC and FDIC if the balanced-budget" amendment is approved.

Bank board general counsel Norman Raiden said he knows of no White House opposition to the formation of the new S&L.

"We have had discussions with OMB and Treasury officials , but they haven't insisted on anything in particular," Raiden said. "They've raised some questions, and we have discussed them."

Gray announced at a Dallas convention of the U.S. League of Savings Institutions that the bank board had approved FADA's charter. An 11-member board of directors, headed by William F. McKenna, chairman of the Federal Home Loan Bank of San Francisco, will run the new Denver-based association, he said.

FADA's job is to sell, at the best possible prices, the properties the insurance corporation was forced to take over from S&Ls that failed because of bad management and the high interest rates they faced in the wake of inflation and deregulation of the financial industry. FSLIC, which has only about $3.2 billion to cover future failures, has allowed many technically broke savings and loans to continue operating because it cannot afford to take them over.

Formation of the new association was the bailout plan favored by many in the thrift industry, who opposed other proposals, including a special assessment of 1 percent of the deposits of all S&Ls and a merger of FSLIC and the larger, stronger Federal Deposit Insurance Corp. The FDIC insures banks.

Widespread industry backing for FADA could put a formidable political barrier in the way of administration efforts to kill or radically alter the new association, said an industry source, who spoke on condition that he not be named. Nevertheless, Reagan aides "are trying like mad . . . to come up with an alternative or squelch" FADA, the source said.

Some directors of the 12 banks in the Federal Home Loan Bank system share the White House's aversion to using the banks' money to capitalize FADA, the source said. Several "have spoken forcefully of their reluctance to put assets" in the new association, he added.