Federal prosecutors are investigating whether a Tennessee defense contractor tried to bribe Rep. William H. Boner (D-Tenn.) by paying his wife $44,000 over a 22-month period when Boner repeatedly contacted government and defense industry officials on the contractor's behalf.

Boner made two out-of-town trips to introduce the contractor, James Wellham, to defense industry executives, and on several occasions Boner and his staff tried to help Wellham with government contract problems. During the same 1982-83 period, Wellham paid Boner's wife, Betty, $2,000 a month to handle various duties for the firm in Washington.

Betty Boner, a lawyer, did no legal work for Wellham, but researched Pentagon grants, explored business opportunities and attended receptions, according to the congressman's spokesman, Jeff Eller. He said she has been unable to document that work because she has lost or discarded her records.

Boner, who has been interviewed by the Federal Bureau of Investigation, said yesterday that he has done nothing illegal and expects the investigation by the U.S. attorney in Nashville to clear him soon. He said he was in no way influenced by Wellham's payments to his wife, adding that he had only done "things that we would do for any other corporate constituent."

But the four-term congressman added in a telephone interview from Nashville: "I did not exercise good judgment. I made a mistake. I should have recognized how it would look in a worst-case scenario. I have nobody to blame but myself."

Boner said Wellham began cooperating with prosecutors when his Nashville firm, American Specialty Metals, came under investigation for selling substandard materials to the Pentagon. The Pentagon is trying to debar Wellham and the firm, which has $474,000 in contracts.

Boner said Wellham "went to the government when he was caught with his hand in the cookie jar and said, 'I've been bribing a congressman. If you give me immunity, I'll give you the details.' " He added, "This guy has been cheating on the government . . . . He has been using my friendship."

Wellham's attorney, John Hollins, said Wellham and Boner were primarily business associates. "It's an ongoing federal investigation and Mr. Wellham is a government witness," Hollins said, adding that he was told the case would be forwarded to the Justice Department. He refused further comment.

According to The Tennessean newspaper, which broke the story last week, Wellham taped conversations with Boner after the FBI equipped him with a hidden recorder. In one conversation at a hotel here, Boner said yesterday, Wellham asked him to intervene in the Pentagon's investigation of his firm; he said he refused. Boner also said Wellham reminded him of the payments to his wife and said that prosecutors would "perceive this as a bribe."

Boner met Wellham in late 1980 after his staff helped American Specialty Metals collect $70,000 in back payments from the Pentagon. A year later, Wellham offered Betty Boner a $2,000-a-month retainer at a time when she was interested in moving here from Nashville to join her husband. Boner says the House ethics committee approved the arrangement.

During the next two years, Boner said, he and his wife flew to Los Angeles at Wellham's expense to introduce Wellham to the president of Hughes Helicopter, a potential customer. Boner also invited Wellham to meet with Lockheed Corp. officials in Georgia.

Boner or his staff contacted federal officials on Wellham's behalf on six occasions, according to Eller. In one case, when Wellham complained of unfair treatment by the Defense Procurement Agency, Boner arranged a meeting with a procurement official in Philadelphia.

In another, when Wellham had supply problems on a $20,000 Air Force contract, Boner's staff contacted the Air Force and Wellham was allowed to retain the contract. Boner also wrote a letter asking the Air Force to consider upgrading Wellham's discharge.

Betty Boner returned to Nashville in the fall of 1982 and joined a law firm that represents Wellham's company. Eller said she still did no legal work for American Specialty Metals, but continued until late 1983 to receive the separate $2,000 monthly retainer for public relations and research. Asked how she could perform those duties without being in Washington, Eller said: "That's between her and ASM . . . A lot of the records she had got lost in the move from Washington to Nashville. It doesn't look good, I admit."

Boner said that Wellham had given him several Christmas and birthday gifts, including a $1,200 hand-tailored suit, and that he had reciprocated with a $1,500 portrait of Wellham. Wellham and his wife also contributed $5,000 to Boner's campaigns and bought Betty Boner a desk and credenza, Eller said.

Wellham has agreed to plead guilty to attempted bribery, The Tennessean reported. The paper also said Wellham has failed an FBI lie-detector test. CAPTION: Picture, Rep. William H. Boner . . . wife received $44,000 from firm.