McCown will go through the NFL's concussion protocol this week. Manziel will start the week working with the first-team offense.
Manziel himself is far from the picture of health. The second-year quarterback, who has lingering elbow soreness, acknowledged after Sunday's loss that the elbow gave him trouble at times against the Jets.
"There were just a few bites here and there, just a little bit of tightness," Manziel said, according to the Akron Beacon Journal. "But other than that, for the majority, to go all the way through the game, it really didn't bother me that much."