Players with 3 accrued seasons enter restricted free agency in their fourth year. If the team chooses to tender the player, they either do so with a first round tender, a second round tender, or a "original round tender." The 1st round tender at $3.91 million is more expensive than the second at $2.746 million, which is more expensive than the original round tender at $1.797 million (all amounts are for 2017 season). All of the tenders allow the team to match any offer from another team (right of first refusal).
Only one other player, Kiko Alonso, received a 1st round tender this year. 12 players received a 2nd round tender.
For a team to pick up a player who has been offered a 1st round tender, they would have to give up their original 1st round pick. So, for example, if Cleveland trades Osweiller to Denver in exchange for Denver's 20th pick of the first round, then Cleveland signs Butler, they would have to give the #1 overall pick to NE, not the #20 they obtained from Denver.
Butler isn't going anywhere. While he is worth a 1st round pick (I'd even be happy to see the Seahawks do that), he isn't worth a 1st round pick, and the 12-13 million per year contract he certainly would demand.
About the only team that I can see pursuing Butler would be Oakland. They have the cap space for a big contract, and they would only be giving up the 24th selection. They need the help in the secondary. They will have to decide whether it is worth gambling on the draft or signing Butler prior to the draft.
After April 21, Butler can only sign with the Patriots. He will definitely sign by June 15 when the guaranteed salary drops from $3.91 million to $660,000.
Butler will receive 6.5x what he made last year, but 1/3 of what he would make if he wasn't a RFA.
Fire Thom Cable