WASHINGTON (AP) _ The chairman of the House ethics committee wants to know why the son of an Illinois congressman was on the congressional payroll while at the same time running for office in Chicago.

Thomas John Savage, son of Rep. Gus Savage, D-Ill., was on the payroll of Del. Walter Fauntroy, the District of Columbia's non-voting representative to Congress, at the same time he was running for the Illinois Legislature from Chicago.

Rep. Julian Dixon, D-Calif., who chairs the House ethics committee, has written Fauntroy demanding an explanation of the younger Savage's employment, a congressional source said Thursday.

A federal investigation into the case began last month after The Associated Press reported Savage was on Fauntroy's payroll although he had submitted a sworn affidavit to Illinois elections officials stating he had met state requirements by living continuously for two years in the legislative district he sought to represent. That period covered the time he was on Fauntroy's payroll.

House rules, meanwhile, require that a congressional employee report regularly to work.

Fauntroy first said the younger Savage had worked on a District of Columbia statehood bill, but Savage later conceded he rarely worked in Fauntroy's office and did little more than stuff envelopes when he was there.

Thomas Savage earned $21,398 while on Fauntroy's payroll from September 1987 through June 1988.

Dixon's letter asked Fauntroy to explain how he had come to hire Savage, what duties Savage performed, and whether Savage had regularly reported to work, the congressional source reported.

A Justice Department official who spoke on condition of anonymity said the FBI also is looking into any connection between Fauntroy's employment of the younger Savage and Rep. Savage's employment of Lezli Baskerville, a former Fauntroy aide.

A month before Fauntroy hired Savage, Ms. Baskerville had been ousted from a job Savage had given her on the House Public Works and Transportation Committee. Committee officials said she had not shown up for work.

After leaving the Public Works panel, Ms. Baskerville returned to Fauntroy's payroll, where she was directed to do legislative work on behalf of the National Black Leadership Roundtable, a private group of black businessmen that Fauntroy chairs, according to a memo provided by Fauntroy to his staff.

Fauntroy, in a statement released Thursday, said: ''On the advice of counsel for the United States House of Representatives, while I have nothing to hide, I have nothing to say.

''It should be noted that no one on my staff has been subpoenaed by any law enforcement authorities, nor has anyone on my staff even talked to any law enforcement authorities.''

The FBI officials investigating the matter do not have subpoena powers, according to sources familiar with the probe.

In addition, congressional sources and others familiar with the investigation said Johnny Barnes, Fauntroy's staff director, refused to meet with FBI agents who attempted to question him. Barnes refused to comment on the matter when telephoned by a reporter.

''I don't know nothing about no investigation,'' Gus Savage told reporters at Chicago's Midway Airport. ''I haven't done anything to get investigated.''

Accusing the assembled media of just wanting ''to make a story,'' Savage testily pointed to one reporter and said: ''Did you stop being a transvestite?''

Contacted by telephone in Chicago on Thursday, Thomas Savage said he was unaware of the investigation. He refused to comment further.

Congress is out of session, and a telephone call to Dixon's office seeking comment on Thursday's developments was not returned.

The FBI conducts a ''preliminary investigation'' after an initial determination that the known facts in a case warrant a more detailed examination. Ordinarily, a report resulting from a preliminary investigation is sent to the U.S. attorney's office for review. A decision then is made whether to present the case to a grand jury.

In the Fauntroy case, the preliminary investigation will determine whether Attorney General Dick Thornburgh will seek the appointment of a special prosecutor, the procedure required when members of Congress are involved.