Politicians from all sides of the Italian political spectrum have their eyes fixed on the new American ambassador here for any hints of the Carter administration's policy toward Italy's powerful Communist Party.

For the Americans, a major impediment to over changes in policy is the sensationalist nature of the Italian press. In the words of one Western diplomat, the news papers here are capable of making headlines out of an American ambassador's sneeze."

It is understood that, to avoid just such press speculation, the new ambassador, Richard Gardner, made a point during his first protocol calls here last month of spending more time with Amintore Fanfani, the Christian Democratic president of the Senate, than with the president of the Chamber of Deputies, Pietro Ingrao, a Communist.

Since President Carter's election there has been speculation in Europe that the U.S. administration might be more flexible toward the Communists than its Republican predecessor. The Italian Communist Party is Italy's second-largest political group and the most important exponent of Eurocommunism, a brand of Communism that professes attachment to Western democracy.

A State Department declaration this month on the U.S. attitude toward Western European Communists was phrased so as to give some Europeans and Italians the impression that Washington might be tolerant of coalition governments that include Communists.

In Italy and France the possibility of Communist participation in coalitions is growing. Earlier this year two U.S. embassy officials in Paris met for the first time with a high-ranking Communist, Politburo member Jean Kanapa.

A first secretary at the Rome embassy has maintained contacts with the Communists in periodic encounters with at least two high-ranking party members. U.S. consuls in Italian cities run by the left also meet with local Communist officials.

The new ambassador, a former professor of international law at Columbia University and a foreign-policy adviser to President Carter during the election campaign, is known to favor amending current U.S. immigration laws to permit increased travel by Communists to the United States.

He is also understood to desire increasing the number of embassy contacts with highly placed Communists, provided this can be done without giving signals of approval of Western Europe's largest Marxist party.

The very idea of changes in policy or style by Ambassador Gardner worries anti-Communist groups here. They fear that any modification of the U.S. position might be seen by Italian voters as an outright endorsement of the Communist Party.

Italy's Communists last polled 34 per cent of the vote, have 221 seats in the 630-member Chamber of Deputies, and participate in the governments of most major Italian cities. Abstention by the Communists on crucial votes gives the essential parliamentary margin of support of the minority Christian Democratic Cabinet.

President Ford and Secretary of State Henry Kissinger took the view that Communist participation in an Italian government was undersirable and would lead to a re-evaluation of Italian-American relations. Former Ambassador John Volpe avoided contacts with Communists as much as possible.

The Carter administration's attitude toward Communists in the government of a member of the Atlantic Alliance appears to be basically unchanged from that of the Ford administration, although Ambassador Gardner may want to make changes in style.

The new ambassador might, for example, include Communist newsmen among Italian journalists invited to the embassy for business. He is also expected to broaden the embassy's cultural activities, which could mean greater contacts with the largely leftist intellectual community.

High-ranking Italian Communist leaders have privately expressed interest in better relations with U.S. policy-makers but have so far refrained from making any overtures.

The Communists are under pressure from extreme leftist students and workers who accuse them of "selling-out" by supporting the Christian Democratic government. A top party member recently said that it is therefore unlikely that the party would publicize any contacts with American officials now.

Expressing the case for increased contacts with the Communists, a conservative American businessman said, "The more we know about them, the better off we'll be." He said the U.S. government should not worry too much that policy changes could give the Communists added respectability "Any party with 34 per cent of the vote is already respectable," he said.