The Justice Department has recommended to the White House that Herman Sillas Jr., the U.S. attorney in Sacramento and a recent candidate for elevation to commissioner of the Immigration and Naturalization Service, be dismissed because he flunked two lie detector tests about taking a $7,500 bribe, according to sources.

The alleged bribe took place in 1974, just before Sillas became state director of motor vehicles. The money allegedly was for restoring an auto dealer's license.

Sillas became U.S. attorney in late 1977. The charge didn't become public until late 1978.

While House officials have known about the problem for more than a month, the sources said, but have delayed taking any action against Sillas, a well-known Hispanic leader in California.

Apparently the White House hoped Sillas would resign quietly, and thus spare the Carter administration the pain of firing a noted Hispanic leader in a pivotal election state, sources said. So far, though, Sillas has resisted any such suggestions, they added.

Lloyd Cutler, the White House counsel, declined to comment on the case yesterday. "I get consulted about proposed appointments and other actions, but can't talk about them while they're pending," he said.

The Justice Department officials conducting the inquiry, Thomas Henderson of the public integrity section, and Michael E. Shaheen Jr., of the department's internal investigations units, also declined to comment on the case.

Sources familiar with the case said they expect an announcement about Sillas's departure soon, perhaps within a few days.

Reached at his home near Sacramento yesterday, Sillas repeated his previous public denial of the bribe allegation. Asked if he was planning to resign he said: "I'm still here. I haven't done anything."

He had no comment when asked if he had been told he'd be fired if he didn't resign. He declined to say whether he was in Washington Friday to discuss his firing. "I had several things to do," he said.

The case against Sillas is being handled administratively, sources said, because the potential criminal case was weak and is now too old to prosecute. In addition, the results of lie detector tests are not admissible in court.

"But he has to go," one source said. "He's the chief law enforcement officer in northern California and people have to know they're dealing with someone of unquestioned integrity. His [Sillas'] integrity is no longer unquestioned."

Two months ago, Sillas was under consideration for the top job in the troubled immigration service. The Carter administration is known to be trying to get a Hispanic to fill the post. Sillas was interviewed about the INS position twice in early November by Attorney General Benjamin R. Civiletti -- while he was under investigation.

A spokesman for Civiletti said only that the two men "didn't discuss the conduct of his [Sillas'] office." He declined to say why Civiletti met with Sillas at all, at a time when the department's "sensitive case" list should have warned the attorney general of the allegation.

In a phone interview yesterday, Civiletti said: "Leaving Sillas aside, a sensitive case report in general is an allegation only. It doesn't say anything about the credibility of the source, or whether a serious investigation is under way."

Other sources said that the Civilette interviews with Sillas occured before the attorney general learned that the California prosecutor had flunked the lie tests. After hearing of the results, Civiletti removed himself from considering Sillas' future and cut off further contacts with him, the sources said.

The bribery allegation against Sillas surfaced in November 1978, when he himself informed the newspaper about news reports of the charge.

Richard Timothy Workman, known by authorities as a professional con man, claimed that he paid Sillas $7,500, through a middleman, in an effort to get his auto dealer's license reinstated in 1974.

Sillas lost a 1974 primary race for secretary of state in California. He then was appointed director of the department of motor vehicles by Gov. Edmund G. Brown Jr.

Sources gave this account of the case:

Authorities didn't take Workman's cahrge seriously at first, but renewed their interest when he passed three lie detector tests on the allegation. Workman never got his license renewed, but didn't make the allegation against Sillas until he was in jail on fraud charges and was seeking favorable treatment.

In mid-November, Sillas agreed to take a polygraph test himself to refute the charges. He failed, but complained about the way the test was conducted, so he took another one in early December. He failed that too.

Shaheen's office then recommended his his dismissal, and Charles F. C. Ruff, then the acting deputy attorney general, concurred. When Sillas refused suggestions that he resign, the department recommendation was forwarded to the White House.

The cloud of the unsettled allegation over Sillas has been especially troubling to the FBI and other prosecutors in California, sources said, because his Sacramento office has been conducting several sensitive investigations, including one about alleged corruption in the state legislature. There have been complaints that Sillas' office has not pushed those inquiries agressively enough.