The person spoke on condition of anonymity Tuesday because the deal was not yet final.
The Pistons hired Stan Van Gundy as their coach and team president last month.
Bower was the coach at Marist College last season, but he resigned that position Monday, and athletic director Tim Murray indicated an NBA job was in Bower’s future.
“I have a lot of respect for Jeff and the job he did in his time at Marist,” Murray said. “He laid the foundation for the program moving forward, and I feel that this is a great opportunity for our next head coach. I wish Jeff the best of luck as he leaves Marist for a very specific and compelling NBA opportunity.”
Bower previously was a general manager and coach in the NBA, holding both those positions with the New Orleans Hornets in 2009-10.
The Pistons have not made any announcement about Bower, although Van Gundy was one of several big names from around basketball who offered praise when Bower was hired by Marist.
“Jeff is a great basketball guy,” Van Gundy said in a statement posted on Bower’s biography on the Marist athletic website. “He was as knowledgeable at what he did as anyone in the NBA and a tremendous talent evaluator.”