The Justice Department is considering a new try at extraditing fugitive American financier Robert L. Vesco from Costa Rica, but reliable sources say that a decision is unlikely for several more weeks.

In the view of some of U.S. officials, such a delay would have the practical effect of enabling Vesco to stay permanently beyond the reach of U.S. law.

At the end of the month, Vesco will have fulfilled a five-year residency requirement allowing him to apply for Costa Rican citizenship. If he does become a Costa Rican national, the odds against a successful extradition bid will be lengthened greatly.

For that reason, State Department officials and some other officials of the Carter administration have argued that the matter be treated with urgency and that a formal extradition request be made by the end of the month.

That possibility officially has been under study for several weeks by the office of Robert Fiske, U.S. attorney for the southern district of New York. However, reliable sources say that Fiske's office has not been handling the Vesco case as a high-priority matter and has not been put under any pressure to do so by Justice Department superiors in Washington.

According to some sources, Justice attorneys seem pessimistic about the chances of an extradition bid and have questioned whether it would be worth the time and money involved. Their pessimism apparently is grounded in the fact that the two previous attempts to have Vesco extraditied, first from the Bahamas in 1972 and then from Costa Rica in 1973, failed.

In addition, Vesco currently is a defendant in a complicated legal suit in the Costa Rican courts and the central figure in a major political dispute within that Central American country. Justice Department attorneys reportedly regard these situations as complications likely to raise additional legal and public opinion bars to extradiction.

Vesco, 41, has been a fugitive from the United States since 1972, when he was indicted on federal charges of making a secret $200,000 cash contribution toward President Nixon's re-election. The charge was that Vesco was seeking to quash an investigation into charges that he had looted the assets of the Swiss-based Investors Overs Services, Ltd., a mutual fund services.

Former Attorney General John N. Mitchell and former Commerce Secretary Maurice H. Stans were indicted on charges of conspiring with Vesco. They were acquitted in 1974. Federal prosecutors attributed the verdict to their inability to have Vesco present to testify.

In 1976, Vesco and six associates were indicted by a federal grand jury in New York on additional charges of conspiring to misappropriate more than $100 million in IOS assets. The suit against Vesco in Costa Rica is Costa Rican citizen who claims he was defrauded of a $224,000 investment in IOS.

Vesco, who has lived in palatial style in Costa Rica, became a close friend and business associate of the coutry's former president, Jose Figueres. It was Figuerees who touched off Costa Rica's current political controversy by giving an interview in April to The New Republican magaine, charging that Vesco helped finance the 1974 campaign of the current president, Daniel Oduber.

That led to the filing of criminal charges against Oduber by a political opponenet, and calls in the Costa Rican legislative assembly for Vesco to leave the country.

This controversy reportedly has led some Justice Department officials to conclude that a request for Vesco's extradition at this time might cause one side or the other to charge the United States with interfering in Costa Rica's internal affairs.

In regard to the possibility of Vesco becoming a Costa Rican citizen, Justice Department sources say it would complicate an extradiction request but not necessarily make it possible.

The extradiction treaty between the United States and Costa Rica excludes the citizens of the two countries from its provisions. But, the sources say, it leaves unanswered and subjec to further interpretation whether this exclusion applies to someone who alledgedly committed offenses in the United States before becoming a Costa Rican citizen.