A Senate subcommittee asked the FBI, Justice and Labor departments yesterday to turn over their files on the aborted three-year criminal probe of Teamsters President Jackie Presser, and to make available for questioning the government investigators who handled the case.

Sens. William V. Roth Jr. (R-Del.) and Sam Nunn (D-Ga.), the ranking members of the permanent subcommittee on investigations, also asked the General Accounting Office to assist in a wide-ranging inquiry into the "lack of coordination" among the law-enforcement agencies.

Government sources said they doubted that Presser's prominent support for the Reagan administration was the key factor in dropping the investigation. These sources said the case was closed primarily because of complications related to Presser's longtime cooperation with the Federal Bureau of Investigation as an informant on other past Teamsters corruption cases.

But Presser's lawyer, John R. Climaco of Cleveland, strongly denied yesterday that Presser had ever cooperated with the FBI. The Los Angeles Times has quoted sources as saying Climaco told ranking Justice Department officials last month that Presser should not be prosecuted because the FBI had made "promises" to him in return for his previous cooperation.

[Last night, the newspaper said it had learned from sources that the FBI gave Presser permission to participate in a payroll-padding scheme in the 1970s involving "ghost employes" and alleged organized crime figures. Climaco and FBI officials declined comment.]

Law enforcement sources said Presser had provided information to the FBI about members of his own union whom Presser had sought to remove. But Climaco called those reports "insanity and lies . . . . My client is not an informant. Never was an informant. Never had a relationship" with the FBI.

Climaco said that he met last month with David Margolis, chief of the Justice Department's organized crime and racketeering section, but that they discussed details of the case and not the alleged FBI-Presser link. He declined to discuss the meeting further.

If Presser was an FBI informant, sources said, questions remain about whether the bureau followed its own guidelines in making a deal with him. "Being an informant does not grant you a cloak of immunity when it comes to obeying the law yourself," a government source said.

Investigators from the Senate and the Justice Department plan to question FBI officials about why the issue of Presser's alleged informant role was not raised earlier in the probe. The investigation focused on allegations that Presser paid off Cleveland union officials in the form of four ghost employe jobs for which they were paid more than $250,000 over several years, without working. Two Teamsters officials have been convicted of receiving payments, which were approved by Presser, who headed a Cleveland union local.

The Los Angeles Times reported 13 months ago that Presser had been an FBI informant.

"This has become a case of government waste," a knowledgeable source said. "Millions of dollars and thousands of man-hours" were spent investigating a case that was potentially doomed from the start because of the FBI's failure to disclose its activities sooner, the source said.