Banner promised in a recent interview with The Associated Press not to put any limits on his search for a new coach.
"It doesn't have to be a college coach," said Banner, who hired Andy Reid during his 19 seasons with the Eagles. "It doesn't have to be a pro coach. It doesn't have to be an offensive guy. It doesn't have to be a defensive guy. I'm more looking for qualities of a person consistent with the most successful coaches."
Shurmur's replacement will be the Browns' sixth coach since 1999.
The Browns were competitive this season under Shurmur. They just didn't win enough.
Cleveland was still in the playoff mix earlier this month, but a three-game losing streak to close the season — they were blown out by Washington and Denver in consecutive weeks — ended any chance of Shurmur saving his job.
Shurmur, who was emotional when he addressed the Browns following Sunday's loss, leaves the team with some satisfaction.
"I am extremely proud of the players on this team, who I felt made tremendous strides and helped to make the Cleveland Browns relevant again," Shurmur said in a release. "I want to thank them, as well as my entire coaching staff for making the past two years enjoyable. My coaches are outstanding teachers and even better men. They helped me lead these players through a unique time of transition.
"This group of players will achieve success soon, and there will be a part of me that will feel very good when that happens."
Shurmur's fate may have been sealed on the first day of training camp in July when Haslam's intent to buy the Browns from Randy Lerner for $1 billion was announced. It may not have mattered how Shurmur did this season because Haslam, a former minority owner with the Pittsburgh Steelers who built his fortune with Flying Pilot J travel centers, was intent on bringing in his own people.