Justice Department prosecutors have recommended that the investigation of national security adviser Richard V. Allen be closed without the appointment of a special prosecutor because the FBI uncovered no evidence he committed a crime in taking $1,000 that a Japanese journalist intended for Nancy Reagan, sources said yesterday.

But Allen's problems within the Reagan White House appear far from resolved, as knowledgeable sources said that a number of presidential advisers are counseling that Allen showed such bad judgment in his handling of the incident that he is a liability and ought to be dismissed.

And the White House appeared to add to its problems by disclosing that presidential counselor Edwin Meese III was told privately by the FBI that its investigation had uncovered no wrongdoing. Other sources said FBI Director William H. Webster told Meese about the case.

This contradicts previous White House statements that officials there had not contacted the FBI. And it also apparently contradicts Reagan administration internal policy that contact between the White House and the Justice Department should be through White House counsel Fred Fielding's office and the attorney general or his deputy.

In Tokyo yesterday, the editor of a women's magazine showed a letter from Nancy Reagan acknowledging a meeting with representatives of his magazine. Details on Page A23.

Meanwhile, a former Reagan aide who said he has not been interviewed by the FBI furnished new details yesterday about Allen's involvement in setting up the interview and making Inaugural accommodations for the Japanese journalists through his consulting firm. The former aide, Peter D. Hannaford, said in an interview from Los Angeles that he visited Allen's consulting offices on Jan. 16. He said he met the three representatives of the Japanese women's magazine huddled with Allen's secretaries, who were busily lining up tickets for them to Inaugural parades and other events.

In addition, Hannaford said he called Nancy Reagan's chief of staff, Peter McCoy, to ensure that a previously requested photo session and brief interview could be arranged. Hannaford said he made the request to McCoy, recommending the Japanese group by telling McCoy that one of the women was an "old friend of Dick Allen's." According to other sources, Allen has told the FBI that he suggested that the journalists seek assistance from Hannaford.

At the time, Hannaford and Allen were in final negotiations for the sale of Allen's consulting business, Potomac International Corp., which Hannaford bought on Jan. 18.

Allen has been hard put to rally support in his defense because of continuing internal criticisms of his overall performance in coordinating national security policy.

Most prominently mentioned within the White House as a replacement for Allen is Brent Scowcroft, the retired general who held the post under President Ford and is now an international consultant here. Others who have been mentioned include Richard Darman, White House deputy to the chief of staff; David Abshire, head of the Georgetown Center for Strategic Studies, and Robert C. McFarlane, counselor to the State Department.

Other officials said that Allen may still survive this crisis because he has an important supporter in Meese.

Sources familiar with the investigation said an FBI preliminary review of the matter has been completed and that attorneys for the department's public integrity section have decided the evidence does not trigger the special prosecutor provisions of the Ethics in Government Act.

Attorney General William French Smith is out of town until next week, however, and no final decision on the recommendation will be made until after he returns, they said.

Participants including the Japanese journalists and Allen's secretary have backed up Allen's story that he merely intercepted the money intended for Mrs. Reagan, officials said.

Intent is a key factor in any potential criminal inquiry and without evidence the money was intended for Allen, there would be no crime.

An early White House statement on the matter said the money was offered to Mrs. Reagan by reporters for the Japanese magazine who interviewed her on Jan. 21, the Reagan family's first day in the White House. Allen said he gave the money to a secretary for safekeeping until he could find the right procedure for turning the money over to the government. Instead, the cash remained in a safe for eight months.

Sources said yesterday that Defense Department officials using the office during the AWACS vote found the cash and turned it over to senior White House officials, who informed the attorney general.

In his explanation of the incident, Allen acknowledged that he had been the initial contact for setting up the interview and passed it on to other officials.

The incident has been complicated from the beginning because the White House has had to correct its statements. First White House spokesmen said Allen had been cleared, only to be contradicted by a Justice Department spokesman who said the matter was still under review.

Tuesday the White House changed its story on when President Reagan had first learned of the FBI inquiry. Spokesmen first said he learned only last week. Now they say he knew since the money was first discovered in mid-September.

That version became confused again yesterday when Reagan startled his advisers by remarking, on the occasion of accepting a live Thanksgiving gobbler from the National Turkey Federation, that the Allen matter had been "investigated" and that "everything was fine."

About five hours later, the White House issued a statement of clarification that said: "The president referred to an initial oral FBI report which was provided to Ed Meese for guidance as to whether any administrative action was necessary. This is the same information that was referred to in the statement of Friday morning, Nov. 13."

This clarification was further clarified by deputy press secretary Larry Speakes. He said that Meese recalls that just after the first of November, an official from the FBI telephoned Meese about the Allen case.

"The FBI felt they could indicate to Ed Meese that no administrative action was necessary" concerning Allen, Speakes said. Meese "presumably briefed the president" on that conversation, Speakes added, and said that was what the president was talking about yesterday.

Last Friday morning, White House spokesman David Gergen initially said that Allen had been cleared of wrongdoing by the Justice Department and that the case was closed. But Justice officials quickly challenged that, saying the case was still under review.

By Friday afternoon, Gergen retracted his original contention, saying instead that the case was still open and that Fielding had mistakenly told him that the case was closed although he had never talked with FBI or Justice officials.