A Long Island construction worker who has been cooperating with federal authorities in a separate investigation of alleged union corruption has sworn that he drew pay from Secretary of Labor Raymond J. Donovan's firm for work he never performed.

Edmund Galke, a member of Local 138 of the International Union of Operating Engineers, said he was paid for five or six days' work on a Nassau County sewer project back in 1972 when he was actually installing wood paneling at the home of a Local 138 official instead.

Galke said he did not know whether officials of Donovan's company, Schiavone Construction, were aware of the incident, but he said it would have been "quite difficult" for the company superintendent on the job "not to have known that I was absent from work for 5-6 days." Galke's account came in conjunction with an investigation of charges that officials of Donovan's firm made illegal payoffs to union leaders.

Schiavone Construction had no comment on Galke's allegation, but the company's in-house counsel, Morris Levin, said the main partner in the joint venture was not Schiavone, but another firm, the Edward Fitzpatrick construction company.

Levin said he was "almost positive" that the superintendent on the job worked for Fitzpatrick at the time although "he ended up working for Schiavone" later on.

Galke's statements were made in an affidavit that his lawyer submitted earlier this week to the special prosecutor in the Donovan inquiry. The prosecutor, Leon Silverman, said yesterday that he would have to determine whether the allegation falls beyond his purview because of the five-year statute of limitations or whether it should be pursued as part of a possible pattern of union corruption that would be within his jurisdiction.

Silverman's inquiry thus far has apparently been limited to allegations of cash payoffs and other favors that Schiavone Construction has been accused of providing to officials of Laborers Local 29 in connection with a series of New York City subway projects. It is a federal crime in most circumstances for an employer to give anything of value to a union official.

Expanding on his account in a telephone interview, Galke said he was working as a machine oiler on a pipe-laying crane in 1972 for a project undertaken by Schiavone Construction and the Fitzpatrick company as a joint venture. One day, he said, Herbert Parmenter, the lead engineer and Local 138 shop steward, "asked me if I would go to his house and do some paneling."

Galke, who said he frequently does carpentry work, said he agreed and installed colored wood-grained paneling in two upstairs bedrooms "and I think a hallway" at Parmenter's home in Northport, N.Y.

"Parmenter told me that he would take care of me and make sure that I got paid by Schiavone for the time that I spent at his house," Galke said in his affidavit. "In fact, I did get paid by Schiavone for the entire period that I worked on Parmenter's house even though I never showed up on the job."

Parmenter, who is still a member of Local 138's executive board, could not be reached for comment yesterday, but he has reportedly denied Galke's account and denounced him as "a chronic liar."

Galke said he has been cooperating with state and federal authorities since 1976 in an investigation of alleged payoffs to officials of Local 138. He said he happened to mention the wood-paneling episode again recently in a conversation with his lawyer, Arthur Z. Schwartz Jr.

Schwartz also represents dissident members of Laborers Local 29, including the main accusers in the Donovan investigation. Schwartz had Galke put his account in an affidavit and submitted it to Silverman.

Silverman, meanwhile, continued calling witnesses before a federal grand jury in Brooklyn. The jurors heard testimony yesterday from Gennaro Liguori, a Schiavone Construction Co. vice president.

Former Local 29 secretary-treasurer Mario Montuoro has charged that Liguori, Donovan and Schiavone president Ron Schiavone were all present at a 1977 luncheon when a fourth Schiavone official--whom Montuoro remembers as "Joe DiCarlo"--handed the president of Local 29 an envelope containing $2,000 in cash.

Ron Schiavone and the company's senior vice president, Joseph DiCarolis, appeared before the jury last week. Donovan, who was executive vice president, has yet to testify. All have denied the alleged payoff.