Bankers and lobbyists strongly support the plan to have some big banks lend money to the fund, since it would help still-struggling institutions avoid another fee.
In a letter to Bair Monday, American Bankers Association CEO Ed Yingling endorsed borrowing from the industry or collecting regular premiums early as alternatives to charging another fee.
An earlier special fee already is having a negative economic impact, and another fee "may do more harm than good," he said.
The FDIC may settle on a plan that combines two or more of the options being considered.
A spokesman for the agency did not respond to requests for comment Tuesday morning. The New York Times reported details of the possible bank lending plan earlier Tuesday.
The FDIC estimates bank failures will cost the fund around $70 billion through 2013. Ninety-four banks have failed so far this year. Hundreds more are expected to fall in coming years largely because of souring loans for commercial real estate.
The FDIC's fund has slipped to 0.22 percent of insured deposits, below a congressionally mandated minimum of 1.15 percent. The $10.4 billion in the fund at the end of June is down from $13 billion at the end of March, and $45.2 billion in the second quarter of 2008.
Bair last week said the FDIC board would meet at the end of the month to consider options including taking Treasury funds, assessing fees on banks in advance and again increasing the fees they must pay.
"We don't want to stress the industry too much at this time, when they're still in the process of recovery," she said.
Congress in May more than tripled the amount the FDIC could borrow from the Treasury if needed to restore the insurance fund, to $100 billion from $30 billion.
The FDIC then adopted a new system of special fees paid by U.S. financial institutions that shifted more of the burden to bigger banks to help replenish the insurance fund. The move cut by about two-thirds the amount of special fees to be levied on banks and thrifts compared with an earlier plan, which had prompted a wave of protests by small and community banks.
Bair had earlier promised a reduction in fees charged to banks if the Treasury credit line could be expanded.
The FDIC emergency premium, to be collected from all federally-insured institutions, is 5 cents for every $100 of a bank's assets minus its so-called Tier 1, or regulatory capital, as of June 30. Banks and thrifts paid an average premium of 6.3 cents last year. A measure of a bank's health, Tier 1 capital includes common and preferred stock as well as intangible assets such as tax losses that can be used to reduce future earnings.
In addition, the FDIC raised the regular insurance premiums for banks to between 12 and 16 cents for every $100 in deposits starting in April, from a range of 12 to 14 cents.