The Patriots haven’t ruled out using the franchise tag before Tuesday’s deadline, but it won’t be for kicker Stephen Gostkowski, Ian Rapoport of NFL.com (on Twitter) hears. Gostkowski, who has been with the Patriots since 2006, is scheduled to reach unrestricted free agency next Thursday. 
The Pats used the franchise tag on Gostkowski in 2015 before signing him to a four-year deal. This time around, Gostkowski may get a chance to shop his reliable leg to other teams, but the Patriots still want to retain him.
Last year, Gostkowski connected on 84.4% on his field goal tries and 98% of his extra point attempts. Because he won’t be tagged, the Patriots may consider the tag for defensive end Trey Flowers or left tackle Trent Brown. Gostkowski’s tag would have cost New England a little less than $5MM, but tags for Brown (~$14MM) or Flowers (~$17.1MM) would be far more costly.
The Patriots have other key free agents set to hit the open market on Thursday including wide receivers Chris Hogan, Phillip Dorsett, and Cordarrelle Patterson, cornerbacks Jason McCourty and Jonathan Jones, and punter Ryan Allen.
I’ve been preaching all along tag Flowers and sign Gost to a multi year deal. Can always tag and trade Flowers if needed but I just can’t see Bill letting Flowers go for nothing
I agree tag flowers, let Trent Brown walk because they have Isiah Wynn to replace him and try to resign Patterson. Hogan, Dorsett can always be replaced!
Flowers would be too big of a cap hit
pats get a compensation pick if flowers signs elsewhere