White House chief of staff Howard H. Baker Jr. and Attorney General Edwin Meese III will meet today in an effort to head off what one senior official said could be "a damaging fight" within the administration over the selection of a Supreme Court nominee to replace Justice Lewis F. Powell Jr.

A senior White House official said last night that he expects Baker and Meese to reach quick agreement and submit a recommendation to President Reagan today. He said the president may be ready to announce his selection by midweek.

Officials said Meese and Baker had talked by telephone over the weekend and agreed it is desirable to present a consensus nomination to Reagan and avoid a battle between conservative and moderate administration factions over Powell's replacement.

"It's important that the president's choice, whoever he is, doesn't become known as Meese's nominee," said one senior official. "That could have an adverse impact on his nomination."

The official was referring to Meese's political problems. The attorney general is being investigated by an independent counsel on conflict-of-interest allegations, and his role in the Iran-contra affair has become increasingly controversial.

Powell's surprise resignation last week has been widely viewed by conservative activists as a last chance for Reagan to advance his "social agenda" opposing abortion and affirmative action. Powell's vote made the difference last year in decisions upholding affirmative action programs and women's right to abortion.

Chief of staff Baker, who is viewed as more moderate and pragmatic than Meese, is said to be emphasizing the importance of selecting a nominee who can be confirmed by a Democratic-controlled Senate, where any Reagan nominee is certain to face close scrutiny. Senior officials have said this could involve regional considerations, since Powell was the only southerner on the court and the support of southern Democrats could be crucial in a confirmation battle.

Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) has already warned that a highly ideological nomination would probably face "big trouble."

But a conservative with ties to Meese said yesterday that the attorney general is "as aware as Howard Baker" of the potential of a bruising Senate fight over confirmation and wants to help the president select a nominee "who would have the best possible chance."

Appearing yesterday on ABC's "This Week With David Brinkley," Meese said that abortion or other social issues would not be "a litmus test." Meese said the president should name someone with strong legal credentials and "probably with extensive judicial experience" whose commitment would be to "interpret the law, not make the law."

This prescription for judicial experience and strict interpretation of the law would appear to fit Robert H. Bork, 60, a federal appellate judge in the D.C. circuit who was passed over for the Supreme Court last year in favor of his colleague, Antonin Scalia. Bork shares Meese's view that a justice should adhere to the "original intent" of the Constitution's framers.

However, Meese said yesterday it would be "inappropriate" for him to comment specifically on Bork or anyone else before making his recommendation to the president.

Bork, regarded as highly competent by other jurists, was solicitor general in the Nixon administration. He fired special prosecutor Archibald Cox during his Watergate investigation after two higher-ranking officials refused to. But sources close to Baker stressed that he had not concluded that Bork failed to meet the test of "confirmability."

There seems little doubt that Meese and Baker, along with White House counsel A.B. Culvahouse, will be major players in recommending a nominee to Reagan.

Baker directed Culvahouse, a longtime associate, to begin preparing a list of potential replacements within hours of learning of Powell's resignation. Meese, who was in West Germany when Powell resigned, telephoned the president on Saturday at Camp David to discuss a replacement for Powell.

Meese, Baker and Culvahouse are to meet today and then confer with Reagan. Senior officials said there is general agreement that Reagan should name a replacement quickly, probably this week, so that the Senate Judiciary Committee can begin confirmation proceedings before the August congressional recess.