Sanchez was pulled from last week's game and backup Greg McElroy led New York to the lone touchdown in a 7-6 win over the Arizona Cardinals.
The Jets are 2-4 in recent games and one of three 5-7 teams overall in the AFC East. New England (9-3) has already locked up the division title.
The Jets have struggled offensively this season. Sanchez has completed 55 percent of his passes for 2,436 yards, 12 touchdowns and 13 interceptions.
He threw three interceptions in the first half of the Arizona game and completed 10-of-21 passes for 97 yards before McElroy took over.
Ryan earlier in the week said he was comfortable with any of his quarterbacks as starters.
In addition to Sanchez and McElroy, the Jets have Tim Tebow on their roster. Tebow was inactive against Arizona because of a rib injury. His availability for Sunday's game at Jacksonville is to be determined.
Notable deaths of 2014 [PHOTOS]