Dennis Thurman, who has been with the Jets for four seasons, is in his first campaign as defensive coordinator.
"From what I'm hearing, there's a lot of positive feelings from owner Woody Johnson to Rex Ryan," Rapoport said Sunday on NFL Network's "NFL GameDay Morning." "It's clear Woody would like him to stay. Two potential issues. I'm told general manager John Idzik is pushing Rex Ryan to make staff changes on defense -- his guys. That can complicate things.
"Rex also wants a contract extension going into the last year of his deal. It is unclear whether Idzik wants to give him one."
The future of Gang Green's coaching position could hinge on whether Ryan gets contracts for his coaching staff -- especially after the defense has performed well this season.