ZURICH (Reuters) - Swiss bank Credit Suisse has started closing down the offshore accounts of U.S. clients who have not declared the money to the U.S. authorities, a newspaper reported on Sunday.

The Sonntagszeitung newspaper said the bank had about 2,500-5,000 U.S. clients with undeclared offshore accounts worth about 3 billion francs, without citing its sources.

The paper said Credit Suisse had started parting company with its U.S. offshore clients, giving them the option of moving their accounts to its CS Private Advisors subsidiary, which would report the accounts to the U.S. tax authorities, or writing them a check.

It quoted an unnamed Credit Suisse manager as saying the bank was only applying the new "zero tolerance" policy in individual cases for now but was considering a more general withdrawal from the U.S. offshore business.

Credit Suisse was not immediately available for comment on the article. Sonntagszeitung quoted a spokesman as declining to confirm the report, but noting the tougher approach of foreign authorities on offshore wealth management in recent times.

"CS sticks to all valid rules and regulations in various countries," a spokesman told the newspaper.

The move comes after rival UBS said last year it would stop offering offshore services to U.S. citizens after U.S. authorities alleged that the Swiss bank has helped rich Americans hide money away from the taxman in Swiss accounts.

A newspaper reported earlier this year that Credit Suisse was writing to its U.S. clients holding Swiss accounts asking them to sign a form that would reveal them to U.S. tax authorities.