President Reagan last week privately assured CIA Director William J. Casey that Casey will be welcome to remain as head of the intelligence agency if Reagan is elected to a second term, informed officials said yesterday.

Reagan gave the assurance by telephone to Casey after Casey sent him a letter to complain about press reports that appeared to originate in the White House saying Casey is ready to return to private life.

In his letter Casey said he has no such desire. The letter made it clear -- though with what one source called "studied indirectness" -- that Casey desired to serve in a second term and did not consider his work as intelligence chief finished.

Asked about the letter and Reagan's reported response, White House deputy press secretary Robert Sims said yesterday: "We never comment on personnel matters, but the president's quite pleased with the CIA and its director."

There has been considerable speculation within the administration that Casey might step down after the election. That speculation has provoked concern among Reagan's more conservative supporters, who consider the CIA director one of their own. However, the prevailing view among Reagan insiders is that the president is unlikely to press any of his Cabinet members for a resignation if reelected.

As governor of California and as president, Reagan has been reluctant to make changes in his inner circle or among his top appointees.

Casey's letter to Reagan had attached to it two clippings -- one from The Washington Times, dated Aug. 30, the other from the New York Post, dated Sept. 4. Both stories said the White House had assembled a list of possible replacements for Casey in a second term.

Casey said reports of this kind hurt morale at the CIA and urged Reagan to stop such leaks, if they were not true.

One knowledgeable official said Reagan then phoned Casey and was sympathetic. Throughout his career and especially as president Reagan has been impatient about leaks to the media from anonymous sources. "It was very clever of Casey," this official said. "He all but got a guarantee that he would stay on. The president said, 'You're my man at the CIA as long as I am president.' "

Casey is one of several senior officials about whose tenure in a second Reagan term speculation has arisen. Others include Secretary of State George P. Shultz, Secretary of Defense Caspar W. Weinberger, White House chief of staff James A. Baker III, deputy chief of staff Michael K. Deaver and Office of Management and Budget Director David A. Stockman. Sources said yesterday that Reagan has made no decision on moves involving any of these.

Casey said yesterday through a spokesman that he would have no comment. But he apparently shared the news about his possible retention with several others and the details of Reagan's call seemed to be known at the senior levels at CIA headquarters yesterday.

Casey's service as CIA director has been controversial, and the virtual promise of continued service in a second term could become a touchy matter in the presidential campaign.

Asked yesterday about the reported assurance that Casey had received from the president, a Senate Democrat who is a critic of Casey said, "All I can say is that Walter Mondale better start printing the Republican bumper-stickers -- 'Reagan-Bush-Casey.' "

A millionaire investor, Casey, 71, has been controversial for both personal and policy reasons. On the personal side, he first refused when named to the CIA to put his extensive holdings in a blind trust as other administration officials have done. He finally did so after he was criticized for continuing to shift his investments while running the agency.

Casey was also in a dispute with Baker over receipt of a Jimmy Carter presidential debate briefing book by the 1980 Reagan presidential campaign. Baker swore under oath that he had received the briefing book from Casey while Casey vehemently denied this. The matter was never resolved as both the FBI and a congressional subcommittee failed to determine how or through whom the briefing book came to the Reagan campaign.

Casey has also had policy disputes with Congress centering on the CIA's role in funding and directing rebellion against the Sandinista regime in Nicaragua. Congressional oversight committees have complained that Casey had not kept them fully informed and Chairman Barry Goldwater (R-Ariz.) of the Senate committee went so far as to send a letter to Casey earlier this year saying "It gets down to one, little, simple phrase: I am pissed off!" This was after disclosures of CIA involvement in the mining of Nicaraguan harbors. Casey later apologized and the mining was halted. Congress has subsequently refused to provide additional funding for the covert war.

At the same time, Casey has generally been popular at the CIA. He has won budget increases that reportedly have gone as high as 15 to 20 percent per year, higher than the much-debated gains in the defense budget. He is frequently credited with having revitalized the agency, much criticized and discredited for assorted misdeeds in the 1970s.

Some officials of the National Security Council in the Reagan White House are critical of Casey, saying that the CIA still fails to provide sufficient intelligence from key areas of the world, particularly the Soviet Union.