McCown will open the season as Sam Darnold's backup.
McCown completed three of eight passes for 26 yards during Thursday's preseason finale in Philadelphia.
McCown is likely to stay in New York after the Jets traded Teddy Bridgewater to the Saints on Wednesday, Jason La Canfora of CBS Sports reports.
McCown once again dressed but didn't play in Friday's 22-16 preseason loss to the Giants.
McCown was in uniform for Thursday's 15-13 loss to the Redskins, but he didn't see the field in the Week 2 preseason contest.
McCown played one series in Friday's preseason opener against Atlanta, completing his lone pass attempt for four yards while adding a one-yard scramble in the 17-0 win.
McCown (hand) will open training camp as the Jets' starting quarterback, Eric Allen of the Jets' official site reports.
McCown (hand) intends to help with Sam Darnold's development while also competing against the rookie for the starting job, Manish Mehta of The New York Daily News reports.
The Jets re-signed McCown (hand) on Tuesday, Ian Rapoport of NFL Network reports.
McCown (hand) could return to the Jets for the 2018 season, NorthJersey.com reports.