"I don't know what's going to happen this weekend so we'll have to see as we go," Shurmur said, via Newsday.
Third-round pick Lorenzo Carter would be in line to replace the 27-year-old Vernon, who was carted off the field on Aug. 26 after his foot was tangled with an offensive lineman during a drill.
Vernon recorded 6.5 sacks in an injury-filled season last year for the Giants, who limped to a 3-13 mark.
Vernon has been shifted to outside linebacker in the team's 3-4 scheme to maximize his pass-rushing skills.
The 6-foot-2, 270-pound Vernon started all 16 games and registered 8.5 sacks in 2016 after signing a five-year, $85 million contract that included $52.5 million in guaranteed money.
A third-round pick of Miami in the 2012 NFL Draft, Vernon notched 29 sacks in four seasons with the Dolphins, including a career-high 11.5 in 2013.