In an unusual expansion of a politically sensitive case, a new federal grand jury here is investigating whether FBI agents made false statements to Justice Department attorneys last year about the FBI's relationship with Teamsters union President Jackie Presser, sources said yesterday.

The broadening of the case from Cleveland, where a grand jury has been at work for seven months, apparently signals that an inquiry into the relationship between Presser and FBI supervisors is nearing a close, the sources said.

The sources, who spoke on condition that they not be identified, said the Cleveland grand jury will continue its examination of why the Justice Department last July abandoned a three-year labor fraud probe of Presser, President Reagan's major ally in organized labor.

The Washington grand jury, they said, will focus on whether one or more FBI agents in the case lied to investigators who asked them, in connection with Presser's role as a government informer, if they had authorized Presser to pad the payroll of his hometown Cleveland local to maintain credibility with organized crime figures.

The new grand jury investigation is taking place, the sources said, because the alleged false statements occurred here and the Cleveland grand jury might not have jurisdiction.

A proposed indictment of Presser on payroll-padding charges, recommended by federal prosecutors in Cleveland, was rejected last summer by Justice Department officials who determined belatedly that such actions by the union chief might have been condoned or authorized by FBI agents in the 1970s.

The Washington grand jury is described as focusing on FBI statements in 1985, when a Justice Department investigation led by Michael E. Shaheen Jr., head of the Office of Professional Responsibility, sought to untangle the precise relationship between Presser and the Federal Bureau of Investigation. It could not be learned whose statements the grand jury is scrutinizing.

Section 1001 of the U.S. criminal code, the statute reportedly under study by grand jurors, carries a maximum penalty upon conviction of five years in prison and a $10,000 fine. It applies to "any false, fictitious or fraudulent statements or representations" made to a federal agency.

FBI Director William H. Webster said in February that he might take disciplinary action against one or more agents who figure in the case. But Webster said he would await the conclusion of the Justice Department investigation.