White House chief of staff James A. Baker III has told a Texas newspaper that Secretary of Labor Raymond J. Donovan should resign, making public Baker's long-held opinion that Donovan is a serious political liability to President Reagan.

"Ray Donovan shouldn't be in here," Baker said in an interview conducted during a turkey shoot on his south Texas ranch during Christmas week. "What's he thinking about? He's got his good name now. He's vindicated. Now he ought to do what's right for the president."

Baker's comments, published Sunday in The Dallas Morning News, brought into the open the dissatisfaction he and others in the White House long have expressed privately about some Cabinet members, particularly Donovan and Interior Secretary James G. Watt. But these Cabinet members have defied attempts to induce them to quit because of their apparent belief that they still enjoy the support of the president.

Yesterday Reagan said he "regretted" the Texas newspaper story, expressed his confidence in Donovan and pronounced the incident closed. Donovan issued a statement saying comments such as Baker's "serve the president poorly, and I work for the president, not his staff."

Baker apologized, to Donovan and to Reagan, that he had been quoted about his dim view of Donovan's usefulness to the administration. But he did not deny the accuracy of the quotation.

"I deeply regret that statements by me in a story in Sunday's edition of The Dallas Morning News reflect unfavorably upon Secretary Donovan," Baker said in a two-sentence statement. "I have apologized to the secretary this morning that such views appeared in the public press, and I assured him that he continues to enjoy the full support and confidence of the president."

Baker said nothing about Donovan enjoying the confidence, full or otherwise, of the White House staff. It has previously been reported, without direct attribution, that Baker wants Donovan replaced.

After a nine-month investigation, special prosecutor Leon Silverman announced last September that he could find "no credible evidence" of ties between Donovan and organized crime, or of other allegations made by various informants and accusers.

Reagan said he took this finding as a clean bill of health for Donovan. The president has since refused the suggestions of Baker and other members of his staff that he find a new secretary of labor.

This has been frustrating to Baker and other politically minded members of the president's staff. Their objection to Donovan is based largely on their judgment that he has almost no support and few relationships within the organized labor movement.

"He brings nothing to us," one White House official said yesterday. "He just draws from the president."

There was talk in the White House many months ago of naming Donovan ambassador to Ireland. But it is not easy to force Cabinet members out because of Reagan's well-known aversion to believing anything negative about those who work for him.

This was displayed again yesterday, when Baker reportedly received an understanding response from the president after apologizing about the Donovan incident. Asked if the president had full faith and confidence in Baker, as well as Donovan, White House spokesman Larry Speakes replied: "Oh, certainly."

In the Texas newspaper interview, Baker also referred to some of his old differences with White House counselor Edwin Meese III. Speaking of the difficulty in getting rid of national security adviser Richard V. Allen a year ago, Baker said: "I can fire the people that work for me, if they screw up. But I can't fire somebody that reports, for instance, to Meese."

Meese, who also has generally supported Donovan, declined comment yesterday. Since Baker's comments to the Dallas reporter, both Meese and Baker have said in interviews with The Washington Post that tensions between them have eased.

Baker's comments about Donovan appeared in the fifth paragraph of a short page-one story in the Dallas newspaper. The article began by saying Baker had become comfortable in his job. It summarized highlights of a 93-inch profile written by Allen Pusey, who accompanied Baker on a two-day turkey hunt during which the chief of staff shot one turkey.

Pusey said there were "no ground rules" for the tape-recorded interview. Although some administration officials said they thought portions of the interview were off the record, Baker appeared to accept the responsibility for his remarks.

Yesterday Baker wrote a wry postscript to a memorandum he issued, attempting to control contacts between White House aides and the press, saying: "The president has refused to make an exception for interviews in turkey blinds!"