Pentagon spokesman Henry E. Catto Jr. intends to leave his post this summer to pursue private business interests in the Washington area, it was learned yesterday.

Catto confirmed that he already has informed Defense Secretary Caspar W. Weinberger that he wants to leave government soon. Catto said neither a date for his departure nor his successor has been decided.

Catto's post of assistant secretary of defense for public affairs is considered crucial to the public promotion of the president's defense policies. The Pentagon spokesman presides over a $33 million public affairs budget, helps decide who should say what about military issues and controls, in part, reporters' access to the defense secretary.

Pentagon insiders predicted yesterday that White House officials will try to name Catto's successor, particularly because President Reagan's defense policy is expected to be a hot issue in next year's political campaigns. Catto's deputy, former New York Times correspondent Benjamin Welles, is considered out of the running for the job because he is a Democrat.

If Weinberger makes the choice for chief Pentagon spokesman, Defense officials predicted that his speechwriter, Kathy Troia, 31, has a chance. Alan Romberg, a deputy assistant secretary of state for public affairs, also has been mentioned.

Catto, a former San Antonio businessman, served as ambassador to El Salvador in 1971, and in 1974 became chief of protocol. In 1979, he became chairman of the Washington Communications Corp., publisher of the Washington Journalism Review.

Although Catto was not a Weinberger intimate nor knowledgeable about defense affairs when he reported to the Pentagon in 1981, there is no indication that Weinberger is pushing him out of the job. To the contrary, knowledgeable sources said, Weinberger has been urging Catto to delay his departure as long as possible.

"Weinberger doesn't really need a spokesman," one administration official said yesterday. "He needs somebody to clean up after him." The official was referring to Weinberger statements that administration officials had sought to soften after they had been delivered.

For instance, Weinberger recently told the American Jewish Committee in New York that it would be "our basic policy" to retaliate strongly if the Soviets or their surrogates in Syria launched attacks into Lebanon. Some administration officials said later that Weinberger had Israeli, not American, retaliation in mind but did not dispute that he had said it would be "our basic policy."

Recently the defense secretary has been angered by statements of some of his deputies, particularly the assertion by Richard D. DeLauer, the Pentagon's research director, that the Trident I submarine missile had exhibited serious flaws in tests. DeLauer disclosed that information before a breakfast group of Pentagon reporters. Weinberger has directed Catto to discourage Pentagon officials from attending such news breakfasts in the future.

"We're on a bad roll," said Catto in explaining why breakfast appearances were being discouraged.