According to Tom E. Curran of NBC Sports Boston, the 35-year-old Gostkowski is not retiring, "and while there has been outside interest, he and the Patriots have made progress toward getting him a new deal."
Gostkowski has spent his entire NFL career in New England, beginning in 2006. He has appeared in 200 games and accrued a career 87.4 field-goal percentage as well as a 98.9 mark on extra points.
The Patriots have kept a few free agents, re-signing punter Ryan Allen, wide receiver Phillip Dorsett, cornerback Jason McCourty and defensive end John Simon.
Gostkowski is a valuable asset given his 13 years of reliability but is especially so following a season that saw several high-profile misses.
Justin Tucker of the Baltimore Ravens missed the first extra point of his career in Week 7, which cost the Ravens the contest, and Chicago Bears kicker Cody Parkey missed what would have been the game-winning field goal in the NFC Wild Card Round (though the NFL later ruled it a block).
Gostkowski missed five field goals and one extra point in the 2018 regular season, and he even missed a field-goal attempt in Super Bowl LIII, but no miss was glaring enough to cost the Patriots.