"Stephen is a unique guy. You don't play for one team for 14 years unless you are," Patriots special teams captain Matthew Slater told reporters. "It's a little bit of an adjustment, obviously. Operationally on field goals it will be different. We'll see how kickoffs go. ... He's meant a lot to this team and you see a lot of that in the record books."
Gostkowski, 35, has served as the Patriots' starting kicker since 2006. He was 7-for-8 on field-goal attempts, but missed four extra points during the team's 4-0 start to this season.
The veteran kicker also handled kickoff duties and was tied for second in the NFL with 21 touchbacks. In his absence, rookie punter Jake Bailey, who has experience with kickoffs, could take over those duties.
The Patriots hosted private workouts for a handful of kickers Wednesday, according to ESPN. New England narrowed its search to 32-year-old kicker Kai Forbath and 37-year-old Mike Nugent.
Forbath, who has spent time with the Washington Redskins, New Orleans Saints, Minnesota Vikings and Jacksonville Jaguars, is 120-for-140 on field-goal attempts in his career. Nugent is 253-for-311 on field goals.