Regulators will begin briefing banks Friday about how they fared in government-performed "stress tests," giving lenders an opportunity to debate the findings before they're made public a week later, the Wall Street Journal reports, citing government officials.

The discussions will signal to some banks whether they'll have to seek additional capital, either from private investors or the Treasury Department, the Journal notes.

Treasury Secretary Timothy Geithner on Tuesday said the government's $700 billion bailout fund has at least $109.6 billion in resources left, and he anticipates that $25 billion will be paid back by borrowers.

Geithner said the "vast majority" of U.S. banks have more capital than they need and that some could be allowed to repay funds distributed under the Troubled Asset Relief Program.

In the stress tests, regulators used some estimates of likely losses on loans that were tougher than observers had expected, the newspaper reports.

The government plans to release on Friday an outline of how the tests were conducted, including the assumptions that regulators used to measure a firm's health. On May 4, some results of the tests are expected to be made public, though it isn't clear exactly how much information will be revealed, the Journal reports.

Of the biggest banks facing government scrutiny, analysts expect JPMorgan Chase ( JPM) and U.S. Bancorp ( USB) to emerge among the strongest. Large regional banks are expected to face the biggest challenges, the Journal reports.

Meanwhile, banks are lobbying the Treasury Department to make it less costly for them to get out of TARP, the Journal reports.

At issue are "warrants" the government received when it bought preferred stock in roughly 500 banks over the past six months as part of TARP, according to the newspaper. The warrants allow the government to buy common stock in the banks at a later date so taxpayers can receive more of a return on their investment when the banking industry recovers.

Many banks want to return their TARP money and, as part of that effort, want to expunge the warrants, the Journal notes. To do that, banks must either buy them back from the government or allow the Treasury to sell them to private investors.

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