The Bush administration may turn to private insurance companies for help in buttressing the shrinking government-run fund that ensures bank depositors against default, officials said.

They said the Treasury Department may start a pilot program that would allow insurance firms to co-insure some bank deposits against loss, in tandem with the Federal Deposit Insurance Corp."It's an interesting idea," a senior Treasury official said. "Maybe we can start it up a bit and see if it can't grow."

FDIC Chairman William Seidman said he expects the bank insurance fund to lose about $4 billion this year. That's double the losses expected just a few months ago and reflects the mounting woes of the nation's banks.

The fund stood at about $13 billion at the end of 1989.

The Treasury is studying a number of ways short of a taxpayer bail-out to cushion the fund against further losses. The fund depends on insurance premiums paid by the banks, but regulators recognize that steep premium increases might only serve to push more banks over the edge.

Other proposals being studied include getting banks to buy interest-bearing, preferred shares in the FDIC or allowing healthy banks to prepay future insurance premiums.

The American Bankers Association, the lobbying group for most banks, also has taken a look at allowing insurance companies to co-insure depositors against loss.

But few, if any, insurance companies seem interested. The insurance industry itself is facing some of the same problems that the banks are, including souring real estate portfolios.

"It isn't clear the insurance industry has the capacity to do a whole lot," said a senior Treasury official.

During the past five years, the FDIC has lost about 10 cents on the dollar after it takes over failed banks and sells them off. Under the ABA study, those losses might be covered through private insurers.

Deposits of $100,000 or less would still be covered by the FDIC. But those above that level could be eligible for private insurance, with depositors paying the premium.

Under current regulations, deposits over $100,000 are not technically insured by the FDIC. But bankers charge that they in effect are covered under the FDIC's "too big to fail" doctrine that effectively bails out all depositors.

"If the concept were 'too big to fail,' that might not be too bad," the Treasury official said. "The notion of what's too big has gotten smaller, that's the problem."

He said the government must have the right to bail out big banks if necessary to protect the integrity of the banking system as a whole but added that that should happen only in rare instances.