Even as UC Berkeley Chancellor Nicholas Dirks has been put on the defensive over his household budget and handling of sexual harassment claims against professors and other campus employees, he has being dogged by an unusual investigation involving the personal trainer he and his wife befriended at the university.

The case stems from a whistle-blower complaint against Devin Wicks, a trainer at the Cal Recreational Sports Facility who has regularly worked out with Dirks and his wife, history Associate Professor Janaki Bakhle. Wicks even traveled as Bakhle’s guest on a two-week trip in January to her native India, paid for by the Cal Alumni Association.

Dirks also received an annual membership at the Cal Recreational Sports Facility valued at $420 from Wicks’ boss — though after questions were raised about the perk, the chancellor paid for his use of the rec center.

Wicks, a $70,000-a-year campus employee, has been on paid administrative leave since April, according to UC sources. That was around the time a whistle-blower made an issue about his ties to Dirks and Bakhle.

Dianne Klein, spokeswoman for UC President Janet Napolitano, declined to comment on why Wicks was on leave, saying the university could not talk about ongoing investigations.

However, after sources confirmed key elements of the inquiry, Dirks spoke to us at length. While saying he was barred from discussing personnel matters, he insisted that he and his wife have acted properly.

The whistle-blower complaint came from a former colleague of Wicks’ who had been fired for alleged embezzlement, sources told us. The complaint raised questions about the personal trainer’s relationship with the chancellor and his wife, including whether all the time he spent working out with them and traveling with her to India was on the campus’ dime.

According to Dirks, Bakhle invited Wicks along on the trip because she was allowed to bring a guest and he was swamped with work. Wicks’ boss said the trainer used his vacation time for the Jan. 2-16 trip.

Wicks did not return our calls seeking comment.

Dirks called Wicks one of the couple’s “oldest and dearest friends” at the university.

The chancellor said he and Wicks have worked out together regularly since they met at a holiday party soon after Dirks arrived at UC Berkeley in 2013.

Wicks and Bakhle spend hours running together, as much as 20 miles at a time, and have run in charity races together, Dirks said.

Mike Weinberger, who retired as the director of recreational sports at UC Berkeley in February, called Wicks an “incredibly valuable person committed to serving the university, and an incredible fitness director.”

Weinberger said it had been his decision to give Dirks a free club membership and to allow Wicks to train with him, “spending as much time as he needed, as reasonably requested by the chancellor.”

“I was thrilled the chancellor would want to spend time in my building and learn about recreational sports, and actually see how many students we serve,” Weinberger said.

He said recreational sports compete with organized athletics for funding, and because “they have all the political clout ... this seemed a very small favor to grant to have a key administrator in our building understanding our services.”

Dirks is dealing with plenty of issues at UC Berkeley. There’s the string of sexual harassment cases, which prompted a stern warning from Napolitano that the campus do better.

Last month, we reported that UC Berkeley has spent more than $1 million sprucing up University House, the chancellor’s official residence, including $700,000 for a security fence and $90,000 for new rugs.

The house’s former manager, Alice McNeil, complained that she had been pushed out of her job after doing chores for Dirks and Bakhle and resisting the couple’s attempts to avoid reporting the value of those hours to the Internal Revenue Service.

The assertions are being reviewed by Napolitano’s office, though it wasn’t immediately clear whether a formal investigation has been opened.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross