Bronx District Attorney Mario Merola has ordered an investigation of possible witness bribery in the criminal case against former labor secretary Raymond J. Donovan, it was learned today.

The investigation was discussed at a secret conference in chambers before Bronx Supreme Court Judge John Collins.

The conference was about a grand jury subpoena that had been issued to one of the lawyers in the Donovan case, Theodore Geiser. He represents Donovan's New Jersey firm, the Schiavone Construction Co.

Merola, who declined to comment, apparently wanted to question Geiser about the contents of a June 24 memo he had written concerning Michael Orlando, the controversial FBI informer who triggered the investigation that eventually led to Donovan's indictment on state charges in the Bronx.

The judge, according to informed sources, was worried that a grand jury investigation might complicate the pretrial hearings he has been conducting since May 20 and ordered the subpoena quashed with the understanding that it could be renewed after the hearings are concluded.

Recounting what appeared to be a penetration of the government's witness security program by a convicted felon "in communication with Orlando," Geiser gave a copy of his "Memo to File" to Justice Department and FBI officials at a meeting in Washington June 26.

"Predictably, Orlando wants to know what's in it for him if he testifies truthfully," Geiser said in the note. He said he regarded this as "tricky and dangerous and that in any case there is no way to nail Orlando down by securing a signed statement. First we have no access and second, he is unlikely to cooperate without cash. I see no way that we would consider this last in any case."

Paul Coffey, deputy chief of the Justice Department's organized-crime section, which sponsored Orlando's entry into the witness program in 1983, sent a copy of the memo to the chief prosecutor in the Donovan case, Bronx Assistant District Attorney Stephen Bookin, on June 28.

Bookin alluded to the situation briefly in open court today in refusing to grant Orlando blanket immunity and thus force him to testify at the pretrial hearings.

In recent weeks, Bookin said, "the district attorney has been investigating information that Orlando may have been solicited for or may have been a solicitor of monetary payments in return for his testimony at this hearing."

Now serving a four-year federal prison term in a special upstate New York facility for protected witnesses, Orlando took the Fifth Amendment 146 times Wednesday, primarily in refusing to testify about a 1978 hijacking that served as the basis for the court-ordered electronic surveillance.

The FBI tapes from that surveillance are now the main evidence in the Donovan case.

Defense lawyers contend that Orlando engineered that hijacking, that his FBI handlers knew he had done so, and that the tapes must thus be suppressed.

The two FBI agents who dealt with Orlando have sworn they had no such knowledge.

In his June 24 memo, a copy of which was obtained by The Washington Post, Geiser wrote of a discussion with an anonymous investigator-consultant "working for us in the Bronx matter." He said the consultant, in turn, had "a client" awaiting sentencing who was "in communication with Orlando."

" . . . Orlando," the memo went on to assert, "says that he was the hijacker and that he kept the FBI agents . . . informed through- out . . . . "

Merola, who declined to comment, apparently wanted to question Geiser about the identities of the investigator-consultant and his informant. Geiser also declined to comment, explaining that he did not want to "risk violating Judge Collins' order" sealing today's in-chambers discussion.

In a telephone interview, the Justice Department's Coffey, who was not bound by the order, took exception to reports that the department did not appear interested in initiating any inquiry of its own. But he refused to discuss the contents of the memo or any federal action stemming from it.

Donovan, who resigned as labor secretary March 15, and his company are accused of defrauding the New York City Transit Authority of $7.4 million on a subway project. Donovan has denied the allegation.