President Reagan, at the request of a top aide, asked Mikhail Gorbachev to autograph a copy of Time magazine with Gorbachev's picture on the cover at the close of the Moscow summit, a spokesman said this week.

White House spokesman Marlin Fitzwater acknowledged a report by the Soviet press agency Tass that Reagan had asked Gorbachev to sign the cover, depicting the Soviet leader as the "Man of the Year."Fitzwater said Reagan was asked to do so by deputy chief of staff Kenneth Duberstein on behalf of an unidentified friend who collects celebrity autographs. Officials were not sure how valuable such a collector's item could be.

Asked if Reagan felt it was a proper thing to do, Fitzwater said simply, "He did it."

Duberstein was not immediately available for comment.

The Tass report was promptly noticed by Time magazine, which ran a full-page advertisement Wednesday in The New York Times, touting the incident. A magazine spokesman in New York said they were "delighted" by the president's move.

"Any time the president of the United States takes a copy of Time to a Russian leader, it's gratifying," the spokesman said. "It's just a delightful thing."

Fitzwater said Reagan asked for the signature while he and the Soviet leader made their official farewells last Thursday and were walking arm in arm down the staircase at the Grand Kremlin Palace.

Fitzwater also said the National Security Council staffers who went to the Soviet Union on advance trips to prepare for the summit took along a dozen photographs of Reagan and Gorbachev, which the Soviet leader autographed for the president to distribute.