Poland has asked its major creditors to lend it an additional $350 million to help pay the interest it owes on $2.4 billion in loans due Western banks at the end of the year, banking sources said today.

Banks holding the notes have insisted the Polish government must pay $500 million in interest before they consider restructuring the overall debt.

Banking sources said today that about 20 banks received the cable from Poland that in effect asked the banks to pay themselves the interest they are owed. It was the first communication from Polish banking authorities since martial law was declared.

Bankers here said they are unlikely to make the additional loan and chances are dimming that Poland and its 460 Western bank lenders will sign an agreement to stretch out repayment of the loans.

Many of the U.S. banks with loans to Poland--such as Citibank, Bank of America, Bankers Trust and Morgan Guaranty--met in New York today to discuss the Polish situation. Bankers familiar with the meeting said no "definitive conclusions" were reached on the Polish loans, but that the banks are not optimistic that Poland will make good on its promises to pay them the interest it owes.

Poland, which declared martial law last Sunday, has survived economically during the last year in part because banks were willing to make concessions on repayment of debt. Because Poland has so many private lenders in the United States, Western Europe and Japan, however, the international negotiations to develop a loan agreement acceptable to all was difficult.

Poland owes about $16 billion to private Western banks and another $10 billion to Western governments. About 60 U.S. banks are owed $1.8 billion, and the U.S. government is owed another $1.8 billion. The biggest chunk of Polish debt is held by West German banks, which were more anxious to reach a debt agreement with Poland than were American banks.

The $16 billion in loans come due between 1981 and 1986. Poland was supposed to repay $2.4 billion this year, but convinced the banks to stretch out the repayment if Poland would pay the interest due. Nearly $500 million in interest was to be paid before the banks would sign off on the agreement. Poland and a task force of the banks were to sign the accord on Dec. 28.

Of the $500 million, U.S. banks are due about $100 million. There have been reports that Poland has paid between $100 million and $150 million already, although major banks refuse to confirm or deny the reports.

"We're still watching and waiting," said one banker. "But we're less than hopeful."