Greenwich Savings Bank, the big New York thrift institution that is close to insolvency, has been put on the block by federal regulators.

New York banking sources said that while the city's big commercial banks probably will make a bid for Greenwich as a courtesy to the federal government, they expect a foreign bank will bail out the nation's seventh-biggest mutual savings bank, which has deposits of about $2 billion.

On Monday, the Federal Deposit Insurance Corp., the government agency that insures deposits in both commercial banks and mutual savings banks, called about 20 New York institutions to a meeting to ask them to consider taking over Greenwich.

"We're looking at the numbers now," said an official of a major New York bank. "But we're not really interested."

Another banker said that his institution, a major one, would make a nominal bid for Greenwich. "But from a strategic point of view, it will be the foreign banks, looking for a greater presence in the United States, that can be expected to bid aggressively for Greenwich," he said. When Franklin National Bank failed in 1974, foreign banks took it over.

Government sources confirmed last Monday's meeting, but said they expected it would be several days, or perhaps a week, before a merger partner is found.

The FDIC announced that it is trying to arrange a merger for Greenwich before the bank comes close to insolvency. "The FDIC's policy is to take steps ahead of time to deal with a potential problem with respect to Greenwich. We are arranging an orderly transaction which will insure that no depositors, whether insured or uninsured, will experience any loss of any principal or interest," the agency said.