The Nets never got the chance to inquire about his interest, because Celtics president of basketball operations Danny Ainge denied the Nets permission to speak to Rivers, reports ESPN.com.
The Nets did not retain interim coach P.J. Carlesimo after they were eliminated from the playoffs by the Chicago Bulls earlier this month.
"Doc has told me he's coming back," Ainge said. "I talk to him almost every day about our team and what we are going to do moving forward. We know people want Doc. We know people want [Rajon Rondo] and KG and Paul Pierce. They are the Celtics. They've all had great success."
Rivers has coached the Celtics for nine seasons, leading them to an NBA title in 2008. He says he understands the challenges with keeping the roster together.
"Well, I don't think anyone is looking forward to [rebuilding]," Rivers said, "but I'm willing to do that. I've had a group that has been very loyal to me, and I think it would have been very easy to just run and go somewhere else and chase something else. ... I just don't think that's the right thing to do. Coaches talk about loyalty and team, and I just thought it was time to show it."