White House officials have asked William D. Ruckelshaus, the first administrator of the Environmental Protection Agency, to take the helm of the troubled agency again, and he has agreed "in principle," administration officials said last night.

Ruckelshaus would head a two-man team selected with an eye to restoring the credibility of the EPA and dealing with its severe internal management problems, according to a proposal made to him this week.

The No. 2 man whom the White House hopes to place in the EPA, officials said, is Walter C. Barber, who served as acting EPA administrator during the first months of the Reagan administration.

Ruckelshaus served as EPA administrator from 1970 to 1973, and quit his post as deputy attorney general in the Nixon administration on Oct. 20, 1973, rather than fire Watergate special prosecutor Archibald Cox in the incident known as the "Saturday Night Massacre." Since 1975 Ruckelshaus has been an executive with Weyerhaeuser Co., a lumber firm based in Tacoma, Wash.

Barber, a longtime civil servant who headed the EPA's air quality planning office during the Ford and Carter administrations, is a civil engineer for Jacobs Engineering Group in Albuquerque. He was interviewed by White House officials this week in Washington.

Officials emphasized that the nomination of Ruckelshaus was "not a done deal." One official said that Ruckelshaus wanted to be certain that "any problems would be worked out" before he took the job.

One of the problems that the White House is looking at--and that is believed to also concern Ruckelshaus--is the possibility of opposition from conservative Republicans, who may question his devotion to the Reagan program of scaling back the regulatory role of the EPA.

Officials also want to be certain that no conflicts of interest arise because of Ruckelshaus' position with an important lumbering firm.

But Ruckelshaus is the first choice of a White House team that, even before the resignation of EPA Administrator Anne M. Burford, was searching for a respected public figure who could manage the agency and end its confrontation with Congress and environmental groups.

"Ruckelshaus brings instant credibility," said one official yesterday. "He has been the front-runner from the beginning. As we see it, there really is no other choice."

Nonetheless, the White House continues to maintain a short list of alternate names in case a snag prevents Ruckelshaus from being chosen.

White House officials settled on the concept of an EPA team, headed by a public figure and backed by a longtime bureaucrat, to resolve the agency's credibility and management problems simultaneously. The twin appointments are intended to signal the public that the environmental laws will be enforced and that the agency will be operated in a non-ideological manner.

Reagan's role in the process was unclear. The president brushed off questions about his EPA choice as he left for a weekend at Camp David.

One official said, however, that the president had been "heavily involved" in the process and had agreed that someone with impressive credentials was needed for the top EPA post.

It was not known when the announcement would be made. Some officials said it could be in the next couple of days, while others said it might take as long as a week.

Whenever the announcement comes, it apparently would end the EPA career of John W. Hernandez Jr., the deputy who became acting administrator after Burford resigned. He was quickly ruled out as a candidate for permanent head of the agency after charges that he intervened on behalf of the chemical industry to soften EPA studies critical of them.

Both Ruckelshaus and Barber are regarded as pragmatists who respect the EPA's mission as a regulatory agency, but who also subscribe to the administration's goals of regulatory reform. Barber has complained to former EPA colleagues about "red tape and the need to cut down regulations," according to one of them.

Neither Ruckelshaus nor Barber could be reached for comment.