Soviet Foreign Minister Eduard Shevardnadze "most probably" will make an official trip to Mexico before the end of this year, and Soviet leader Mikhail Gorbachev may come next year, Mexican officials said today.

The expected trip by Shevardnadze, which would mark the first visit to Mexico by a Soviet foreign minister, was described here as part of a new Soviet effort to improve relations with Latin American countries. The Soviets "are trying to make relations closer, to show friendship," a Mexican official said.

The leftist-oriented Mexican newspaper La Jornada, which reported Sunday that Shevardnadze was coming here in September and that Gorbachev would visit next spring, said that Gorbachev also would visit Cuba, Nicaragua, and possibly Brazil, Argentina and Peru. There was no immediate confirmation of Gorbachev's plans to make such a trip, but two well-placed sources indicated that the Soviets had provided the newspaper with the bulk of its information.

"This is a general tendency on the part of the Soviet Union. It is trying to move closer to Latin America," a diplomatic source said.

It seemed likely that the United States would be displeased if the Mexicans receive a top Soviet leader. The State Department was quick to express concern late last year over reports, which proved to be untrue, that a Soviet ship was planning to visit a Mexican port.

The United States already is unhappy with Mexico's diplomatic tilt toward Nicaragua's Sandinista government, and with its record of votes against Israel and South Africa in the United Nations. A U.S. Embassy spokesman declined to comment on the possibility of a high-level Soviet visit to Mexico until it was confirmed.

Both the Mexican Foreign Secretariat and the Soviet Embassy have declined to comment publicly on the La Jornada report. "These things are usually announced simultaneously in both countries," a Foreign Secretariat official said in explaining the delay.

Mexican officials said privately that Shevardnadze most likely would visit Mexico sometime this year, but that there has been "no definite decision" on a trip by Gorbachev. "There have been talks about the possibility," a Mexican official said.

The Mexican officials said that a trip by Shevardnadze would come as part of "normal diplomatic activities" and denied that it would signal a change in Mexican policy.

"The fact that we haven't had a Soviet foreign minister here in the past doesn't mean that we can't have one in the future. Mr. [George] Shultz the U.S. Secretary of State has come here a dozen times," a Mexican official said.