Vernon missed a second straight practice Friday due to an ankle injury and head coach Pat Shurmur acknowledged he will not be available against visiting Jacksonville.
"It's safe to say that Olivier Vernon isn't going to make it this week," said Shurmur, via the team's official Twitter feed. "He's making progress and we'd love to have him on the field."
Vernon sustained a high-ankle sprain on Aug. 26. He was carted off the field after his foot was tangled with an offensive lineman during a drill.
Third-round draft pick Lorenzo Carter is the likely replacement for the 27-year-old Vernon, who recorded 6.5 sacks in an injury-filled 2017 season for the Giants.
Vernon has been shifted to outside linebacker in the team's 3-4 scheme to maximize his pass-rushing skills. Jason Pierre-Paul, who signed with the Tampa Bay Buccaneers in the offseason, led New York with 8.5 sacks in 2017.
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.
Carter recorded 14 sacks in four seasons at Georgia, including 4.5 in 2017 as the Bulldogs advanced to the national championship game.