U.S. officials are offering 11 Swiss banks -- Credit Suisse among them -- a deal that would allow them to avoid criminal prosecution in exchange for revealing full details of their U.S. offshore business to Washington, a paper reported on Sunday.

Famed for the care with which it protects account holders' anonymity, the Alpine state has been forced to act by a series of U.S. probes into alleged tax evasion by Americans concealing their assets in Swiss banks.

In 2009, the Swiss parliament approved a deal to allow UBS to reveal details of about 4,450 U.S. clients and pay a $780 million fine to end lengthy tax proceedings that had threatened the future of the country's biggest bank.

The Swiss government has been in talks with U.S. authorities for months to try to get an investigation into 11 banks dropped, in return for expected hefty fines on the banks and the handing over of the names.

Credit Suisse, Julius Baer, and Basler Kantonalbank are among the banks under investigation.

Citing an unnamed source, the newspaper SonntagsZeitung reported that 11 banks would each be offered a deal like the one to which UBS agreed.

In exchange, the banks would have to accept U.S. requests for administrative assistance in tax-evasion cases, which would mean delivering all information on their U.S. offshore business via Bern to the United States, the paper reported.

The paper said the banks would likely accept the deal.

Moreover, as part of an agreement, the names of the U.S. clients would be blacked out and the banks would also be fined, the paper said, adding that the banks had until Tuesday to agree to the terms in writing.

According to the paper, the information the banks would have to hand over included:

-- Correspondence between a bank and its U.S. clients, including notes from telephone conversations and meetings.

-- Internal notes about U.S. client business from the relevant business units and management

-- Correspondence between banks and third parties, such as independent wealth managers concerning U.S. clients

-- All documents about the U.S. business model and about U.S. funds that were transferred to third parties.

The paper said the 11 institutions would have to reveal the names of the bankers who conducted the offshore business, though criminal cases against individuals would not be taken up.

Credit Suisse, Basler Kantonalbank, and HSBC Switzerland would have to deliver material by Dec. 31, the paper said.

A Credit Suisse representative declined to comment. The Swiss Bankers Association was not immediately available for comment. Neither was a representative of Julius Baer.

A spokesman for the State Secretariat for International Financial Matters, which has represented the Swiss government in negotiations with the United States, was also not immediately available.

(Reporting by Catherine Bosley; Editing by Jon Loades-Carter)