After a decade of chill between Moscow and the Italian Communist Party, the biggest in the West, a thaw appears to be developing under Soviet party leader Mikhail Gorbachev.

That, at least, is the interpretation being given here by politicians on the eve of the departure for Moscow of Alessandro Natta, leader of the Italian Communist Party for the past 1 1/2 years.

Except for ceremonial visits for funerals of Soviet leaders, no Italian party head has visited Moscow for private bilateral talks in at least five years -- since relations became frigid after the Italian party's criticism of Soviet policy in Afghanistan and Poland at the beginning of the 1980s.

Natta succeeded the late Enrico Berlinguer, whose Eurocommunist independence brought relations with Moscow just short of the breaking point.

Now, however, the enthusiasm with which the Italian party press and officials have greeted Gorbachev and his reformist policies clearly suggests a change in how the Italian Communists view the Soviet Union.

Italian party officials privately insist that Natta's visit, beginning Sunday, in no way represents a reversal of Berlinguer's criticisms of Moscow's policies, especially on Poland and Afghanistan, but represents a new dialogue between "fraternal communist parties."

The new dialogue, party sources here say, owes everything to the fresh image of Soviet communism projected in Europe by Gorbachev since he succeeded Konstantin Chernenko last year.

It is an image Gorbachev had apparently launched when, as Chernenko's deputy, he headed the Soviet Union's delegation to Berlinguer's funeral in 1984.

The differences between the Italian and Soviet parties are longstanding, going back at least as far as the more liberal brand of communism advocated in the 1920s by Antonio Gramsci, the founder of the Italian party.

But Berlinguer brought it to a head at a meeting of communist party chiefs in Berlin in 1976 when he proclaimed his party's "autonomy and independence" from Moscow. Then he further heightened tensions in 1980 by his criticisms of the Soviet invasion of Afghanistan and of Poland's 1981 proclamation of martial law and crushing of the Solidarity labor movement.

According to party officials here, Natta hopes to explore the depth of change in Moscow under Gorbachev and to learn more about the Kremlin's real intent in Afghanistan and Gorbachev's recently announced disarmament policy, which has been received with great interest here.