In a carefully worded statement, the White House cleared the way yesterday for the likely resignation of Herman Sillas Jr., the U.S. attorney in Sacramento. The Justice Department recommended last December that he be fired because he flunked two lie-detector tests about allegations that he had taken a bribe.

Sillas' fate has been a delicate political issue at the White House for months because of his popularity with Hispanics.

Though White House and Justice Department officials refused to comment on the statement, Sillas immediately said he had been "cleared" of any allegation of wrongdoing and now could consider resigning.

The controversy arose in 1978 when a California car dealer told authorities that he had given Sillas a $7,500 bribe in 1974, just before Sillas became state director of motor vehicles.

The car dealer passed lie-detector tests of the accusations, while Sillas failed twice. Acting deputy attorney general Charles F. C. Ruff recommended dismissal Dec. 20, after Sillas refused to resign.

White House counsel Lloyd Cutler reviewed the Justice case file and gave Sillas an opportunity to rebut it, but asked in July that Sillas take a third lie-detector test. Sillas responded by holding an extraordinary news conference in Washington July 15, refusing to take another test and all but daring the White House to fire him.

In the statement issued late yesterday afternoon, the White House said Cutler had concluded that the "allegations against Mr. Sillas have not been proven. An unproven allegation, of course, should not damage Mr. Sillas' good reputation."

Sources have said that Justice never concluded that the allegation was true, just that Sillas' failure to pass the lie-detector tests raised such serious questions about his integrity that his firing was recommended.

The White House statement said the Cutler report, which President Carter approved, also concluded that the "necessary relationship of mutual trust and confidence between the Department of Justice and Mr. Sillas as United States attorney has been impaired to the point where either or both may wish to discontinue the relationship."

It is clear that Justice officials wished to discontinue the relationship last Dec. 20. Cutler asked Sillas yesterday to "examine his position in light of these conclusions" before Cutler advises the president further on the matter.

Sillas said in a telephone interview from Sacramento yesterday that "the cloud has been removed. I am grateful to the president and to his staff for some form of due process."

He said it was a "fair statement" to say that his relationship with Justice had been impaired and added that he planned to take a few days off and consider his options, including resignation.

Sillas, who once was considered for the post of commissioner of the Immigration and Naturalization Service, said he never would have considered leaving "with a cloud over my head."

Several Hispanic groups rallied to Sillas' side and said that there would be political repercussions for the Carter administration if he were dismissed. Some Justice officials thought that the lengthy delay in dealing with the recommendation was based on such political considerations. Cutler denied it.

Yesterday's statement did not address Cutler's response to Sillas' July 15 refusal to take a third lie-detector test or his open challenge to the White House.