There will also be another change on the depth chart with Drew Stanton expected to be the backup to Mayfield, this year's No. 1 overall draft pick.
Mayfield relieved an injured Taylor and helped Cleveland erase a 14-point deficit in a 21-17 victory over the Jets in Week 3. The win was the first for the Browns (1-1-1) since they defeated the then-San Diego Chargers on Dec. 24, 2016.
Taylor will accompany the team to the West Coast but he was limited again in practice on Friday. Stanton has taken all the reps at backup this week, Cleveland.com reported.
"He's been tremendous,'' Browns offensive coordinator Todd Haley said of Stanton. "He's a unique, unique quarterback. He has insight that I haven't seen from very many guys. He has a unique feel for how to deal with Tyrod and how he deals with the young guys. It's a great situation for a young guy to be developing in.''