Bank of America Corp. is said to need $34 billion of capital to withstand a deep economic downturn, and Citigroup Inc. may need as much as $10 billion, Reuters reports, citing a person familiar with the matter.

About 10 of the 19 big U.S. banks being stress-tested may need more capital, a person familiar with the official talks has said.

The sources were not authorized to speak because the banks’ stress test results have not yet been made public. Results are due late Thursday.

Goldman Sachs Group Inc., Morgan Stanley, MetLife Inc., JPMorgan Chase & Co., Bank of New York Mellon Corp. and American Express Co. were alleged not to need additional funds.

“The markets are telling us we’re in a recovery and the banks are beginning to heal,” William Isaac, former chairman of the Federal Deposit Insurance Corp., said in an interview today. The end of the stress tests after “three months of water torture” is providing investors some relief, he said.

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