Quinn was instrumental in creating a strong defense for the Seahawks that became the cornerstone of their Super Bowl-winning side, with some suggesting that the defensive unit is among the best in NFL history.
The Browns were said to have been interested in Quinn, but decided not to wait until Seattle's playoff run was over, instead hiring Buffalo Bills defensive coordinator Mike Pettine as head coach last month.
Quinn did have an interview with Cleveland but turned down the option of a second until after the Super Bowl, prompting the Browns to take action and move for Pettine.
"I certainly would've been interested. I mean, it's a big-time place. It's the Cleveland Browns," Quinn told the Cleveland Plain Dealer.