Washington is inching closer to a full-scale invasion from the nation's largest banks, with Citicorp and Chase Manhattan being the two most often mentioned by banking officials as bidders for the District's second-largest thrift institution, National Permanent Bank.

The Federal Home Loan Bank Board began seeking buyers for National Permanent Feb. 1 to restore financial health to the failing institution, and bids by potential buyers must be submitted within the next 10 days.

Local bankers speculate that Citicorp's and Chase's interest in the troubled thrift could mean the banking giants are trying to sidestep District laws that require any out-of-state institution that buys a bank here also to invest millions of dollars in the District.

The investment requirement does not apply to the acquisition of savings and loans. But bankers point out that such a ploy to buy a thrift to avoid investment laws could cost money-center banks dearly in tarnished public image.

The banking giants from money centers such as New York lobbied hard to persuade the City Council to pass a law allowing them to establish full-scale banking activity in the District through the acquisition of local banks. The council passed such a law Jan. 15 with amendments requiring out-of-state buyers to invest between $50 million and $100 million here, create 200 jobs and set up at least two new branches in underserved areas.

Citicorp lobbied particularly hard for the law and used the lure of sizable investments to help convince the council that the entry of banks from money centers would benefit all sectors of the local economy. Thus, using a loophole could generate an adverse reaction here.

Charlene Drew Jarvis (D-Ward 4), who drafted the amendments requiring economic investments in return for permission to buy a District bank, said that Citicorp officials have promised to make the investments "regardless of whether they enter with a thrift or a bank."

Citcorp spokesman John Maloney said, "We hope to make the purchase of a bank in Washington and honor our commitments that way." But he stopped short of saying that Citicorp would honor the economic-investment commitments if Citicorp, the nation's largest bank, were to buy a thrift and not convert it to a bank.

Speculation runs high for other possible combinations that will result from the District's new law. Local banking sources also said Chase is looking closely at Palmer National Bank. Neither Chase nor Palmer would confirm or deny the possibility of a merger. Palmer's investment banker, Alex. Brown & Sons Inc. in Baltimore, said it had not heard the rumor but said such a merger "would make sense."

Federal regulators put National Permanent up for bid because, by their accounting rules, the thrift had only $1,000 of net worth -- the difference between assets and liabilities -- at the end of 1985.