White House counselor Edwin Meese III said yesterday that Richard V. Allen's return as White House national security adviser would be influenced, but not necessarily determined, by the Justice Department report on his dealings with Japanese journalists.

Meese also told a group of reporters that he does not think the Allen case requires appointment of a special prosecutor. Under existing law, that decision is the responsibility of the attorney general, William French Smith.

Meese said the current FBI investigation of Allen "will obviously be a factor" in his fate. Allen requested "administrative leave" Sunday to defend himself against charges of impropriety in accepting $1,000 from a Japanese magazine team that interviewed Nancy Reagan after the inauguration last January.

Last night in Cincinnati, when asked whether Allen would be staying on, President Reagan said, "We'll have to wait and see the outcome of this."

As Allen sped through a morning-to-night round of interviews explaining his actions yesterday, Meese said he would "look at the whole business," including Allen's dealings with clients of his former consulting firm in deciding whether to restore his White House status.

"I see no reason why he shouldn't" come back if he is cleared of charges by the Justice Department, said Meese, adding that he would make his own judgment on reinstating Allen, "subject to concurrence by the president."

Meese, Allen's immediate superior on the White House staff and reportedly his strongest defender, walked a narrow line under persistent questioning from reporters. He said it was "appropriate" for Allen to arrange the interview with Mrs. Reagan, for him to lunch in the White House mess with a former business client from Japan and to receive delayed payments until this month from the purchaser of his business-consulting firm.

But Meese also left room for a judgment against reinstating Allen in his old position, even if he is cleared of any criminal charges by the Justice Department. Meese said the Allen controversy is "an unfortunate thing" that "certainly has not been helpful" to the administration, adding that Allen's decision to step aside, at least temporarily, "was the right thing to do."

In recounting his part in last weekend's developments, Meese disclosed that he had turned over to the Justice Department some "other documents" in addition to the $1,000 cash in an envelope found in a safe in an office Allen had used.

Allen has said he intercepted the envelope as the Japanese journalists tried to give it as a gratuity to Mrs. Reagan, had his secretary put it in the safe and forgot about it.

Meese would not describe the "other documents" but said they were "no big deal." Allen has said the other papers he was handed by the Japanese journalists consisted of copies of the Japanese women's magazine, photostated copies of the magazine's previous interviews with other First Ladies and a one-page cover sheet explaining in English about the magazine and the previous interviews.

As Meese was meeting reporters over breakfast, Allen was being chauffeured from the NBC to the CBS television studios to appear on the networks' morning programs. Last night, he appeared on ABC-TV's "Nightline" program, and this morning he planned to meet with the same reporters who interviewed Meese yesterday.

Meese, a former California prosecutor, explained why he had taken the evidence found in Allen's safe to the Justice Department, rather than asking his subordinate for an explanation of the money.

"I was following rules and procedures," he said, "and the highest ethical standards." To do otherwise, he said, would have "contaminated the evidence" and risked charges "of a cover-up."

Meese also told reporters they were wrong to have reported that he sought to save Allen's job when the other two members of the White House "Big Three," James A. Baker III and Michael K. Deaver, wanted him fired.

Meese said no one was "eager to push him Allen over the side" but conceded that the other two senior aides "might have felt even more strongly . . . the same concern I have that it not damage the president."

Allen said Sunday that he is no longer receiving deferred payments from Peter D. Hannaford for purchase of Allen's former international consulting business because in the last few days the former Reagan aide and speech writer has paid the outstanding debt of about $50,000.

Deaver, meanwhile, also has received deferred payments from Hannaford, who purchased Deaver's 40 percent share of what used to be their jointly owned consulting firm, Deaver and Hannaford Inc. The deferred payments are noted in Deaver's financial disclosure statement, prepared last Feb. 19.

On Air Force One yesterday as the president flew from California to Cincinnati, deputy White House press secretary Larry Speakes said Deaver got a final, lump-sum payment in July for his share in the consulting firm.

Speakes said any suggestion that Deaver is still getting payments from the sale is "dead wrong."