VATICAN CITY (AP) _ Soviet leader Mikhail Gorbachev has written to Pope John Paul II to arrange a historic meeting between the two men and discuss troubled Vatican-Soviet relations, a senior Vatican official said Friday.

In Moscow, Soviet sources said Gorbachev is expected to visit Italy beginning Nov. 25. Italian officials have indicated Gorbachev may tour several cities.

A meeting between Gorbachev and Polish-born John Paul has been viewed as likely during the Soviet leader's stop in Italy but there has been no confirmation by either side.

Such a meeting would be of historic proportions, the first between the leader of the world's 850 million Roman Catholics and the head of a Soviet party that disparages religion.

John Paul, speaking to reporters earlier this year, said he would be willing to receive the Soviet president.

The Vatican official, speaking on condition of anonymity, said Gorbachev referred to a possible meeting in a letter delivered to the pope last month by Yuri Karlov, an aide to Soviet Foreign Minister Eduard Shevardnadze.

''The letter said in effect 'let's talk business''' said the Vatican official.

The letter was in response to one written by the pope to Gorbachev and carried to Moscow in June 1988 by Cardinal Agostino Casaroli, the Vatican's secretary of state, the official said.

Casaroli led a delegation of top Roman Catholic officials to Moscow for a celebration of the Russian Orthodox Church. The visit signaled an improvement in historically icy Vatican-Soviet relations.

Further progress has been made this year, capped by the Vatican appointment of a bishop in the Soviet republic of Byelorussia, the first bishop there since the aftermath of the Russian Revolution.

In August, John Paul held long talks with Karlov when the Soviet envoy met with him at his Castel Gandolo vacation retreat south of Rome. At that time, Vatican spokesman Joaquin Navarro said the two discussed ''issues of common interest, such as religious freedom and peace in the world, with particular reference to the Middle East.''

Chief topics for a Gorbachev-pope meeting, the Vatican official said, would be the Baltic states of Latvia and Lithuania, where there are large numbers of Roman Catholics, and the status of the Ukrainian Catholic Church, which is a major stumbling block to improved Vatican-Moscow ties.

The Vatican does not recognize the annexation of Lithuania by the Soviet Union in 1940, and a Lithuanian exile mission is accredited to the Holy See.

The Ukrainian Catholic Church was forcibly merged with the Russian Orthodox Church under Soviet dictator Josef Stalin in 1946. But there is a strong underground Ukrainian church and Ukrainian faithful have been carrying out public protests seeking official recognition of their church.

The pope also has expressed a desire to visit the Soviet Union provided he could meet with his flock throughout the country. But Vatican officials said such a trip is not expected in the immediate future.