President Reagan yesterday appeared to hold out the threat of new action against Cuba to counter growing Soviet arms shipments to Havana.

The president, reported by advisers to be planning a speech soon dealing with Cuba, said Secretary of State Alexander M. Haig Jr. raised Soviet arms shipments with Soviet Foreign Minister Andrei Gromyko in their meetings this week at Geneva.

"We know that Cuba is a stooge for the Soviet Union," Reagan said in an interview with Dan Rather of CBS News. He refused to rule out a U.S. embargo of Cuba or any other step and said:

"I would think that Cuba, if it was smart, would take another look and see if it didn't want to rejoin the Western Hemisphere."

Reagan also confirmed reports that Haig met secretly last November in Mexico City with Cuban First Vice President Carlos Rafael Rodriguez. State Department officials have been saying that to their knowledge the meeting never took place, and other officials expressed surprise last night that Reagan had confirmed the meeting.

Reagan said it occurred before the "size of the arms buildup was apparent," and came partly in response to "certain queries that had come from Cuba, indications that maybe they had something they wanted to say."

Asked if the Cubans had said anything, the president replied, "Not loud enough."

The president generally defended his foreign policy and said he had talked to former secretary of state Henry A. Kissinger after reading Kissinger's criticism of Reagan's policy on the Polish crisis. "We're not all that far apart," Reagan said.

Reagan reiterated that he is considering further steps against Poland and the Soviet Union if the situation does not improve.

On domestic policy, the president said he will be submitting budget deficit estimates for coming years only because he is required to do so. When he makes such estimates beyond the current year, Reagan said, "I don't believe what I'm saying. There are so many imponderables that no one can properly project more than the immediate year in advance."

Reagan said he had meant only to be "completely neutral" when he declined to respond to a question at his last news conference about whether he agreed with members of Congress who have called for the resignation of Federal Reserve Board Chairman Paul A. Volcker. "He's a good professional," Reagan said.

He blamed the media for giving a distorted image of his administration's attitude toward blacks and the lifestyle of Nancy Reagan.

Reagan said some parts of the media have built an image of him as a "hardhearted" man with "a tinge of racism." His administration is working to help blacks, he said.

His wife has gotten a "bum rap" from the media and is doing nothing that Jacqueline Kennedy Onassis did not do in trying to make the White House "the prettiest house in America," Reagan said.