The Federal Deposit Insurance Corp. said yesterday it will try to claim a major share of the $750 million that Drexel Burnham Lambert Group and deposed junk bond king Michael Milken have agreed to give back to victims of illegal transactions in high-yield securities.

The FDIC and the Resolution Trust Corp. -- the S&L cleanup agency -- disclosed they have formed a special task force to try to recover some of the money that failed savings and loans lost in what officials described as "daisy chain" deals with Milken and Drexel.

As part of the settlement of charges brought by the Securities and Exchange Commission, Milken has agreed to put up $400 million and Drexel $350 million as restitution to investors who lost money as the result of illegal actions.

For months, the FDIC, which provides much of the manpower for the S&L cleanup, and the SEC have been investigating an elaborate series of transactions involving a group of high-flying savings and loans that did business with Drexel and some of Wall Street's best-known corporate takeover artists.

That investigation is still underway, FDIC General Counsel Alfred Byrne said yesterday, but "we have preliminary information that links Drexel and Milken to millions of dollars lost by a number of failed thrifts in junk bonds." Any money recovered will reduce the cost to the taxpayers of the S&L cleanup.

The Washington Post reported in February that Drexel, the corporate raiders and a group of savings and loans bought each other's bonds, gave each other loans, traded securities back and forth, worked together on real estate deals and corporate takeovers and sometimes allegedly helped each other manufacture phony profits and evade regulatory requirements.

Of the 10 thrifts that were the largest investors in junk bonds, eight were created or purchased with junk bonds issued by Drexel. Drexel raised more than $1.2 billion in capital for the group of S&Ls, which, in turn, bought $10 billion worth of junk bonds from Drexel. Drexel and Milken also were part-owners of two of the junk bond thrifts, Lincoln Savings and Loan of Irvine, Calif., and Columbia Savings of Beverly Hills.

Most of the S&Ls that were the biggest investors in junk bonds have gone broke and been taken over by the government, leaving the RTC holding junk bonds with a face value of about $3.8 billion. Those bonds today are worth only about 50 cents on the dollar, said Kenneth H. Thomas, a Miami banking consultant and specialist in thrift junk bond investments.

By Thomas's calculation, the S&Ls taken over by the government have lost about $1.9 billion on their junk bonds, although not all those bonds were bought from Drexel and not all the losses on Drexel junk bonds were due to illegal actions by Drexel.

The government's losses are certain to grow, Thomas said, because Columbia Savings, the biggest junk bond S&L of all, is also believed likely to be taken over by the government. Columbia alone held junk bonds with a face value of $3.7 billion as of Dec. 31.

Claiming part of the $750 million restitution fund "is going to be fruitful" for the government, Thomas predicted. "I see another purpose," he said: "to expose the true extent to which one financial institution -- Drexel -- and one person -- Milken -- exerted influence over all these institutions."

In order to claim any part of the Drexel and Milken restitution funds, the FDIC will have to show not only that failed S&Ls lost money on junk bonds bought through Drexel, but also that the losses were linked to illegal activities, SEC and FDIC officials said yesterday.

"Our people have found what they believe to be wrongdoing," said FDIC's Deputy General Counsel Jack Smith. "We will be examining our options and formulating our legal theories."

The FDIC is not the only one lining up for a share of the Drexel-Milken fund. A federal court will decide who will receive money and how much.