Scott Merryfield
Senior HTF Member
While it's not exactly the same as the NBA's "Larry Bird rule", the current NFL agreement does allow a team to place a franchise tag on one player which effectively prevents him from becoming a free agent, as well as guaranteeing the player a certain salary based on the top players at his position. There is also a "transition" tag, which gives the team the right to match an offer from another team.
The main difference from the "Larry Bird rule", though is that teams must still fit these franchise and transition salaries under their fixed salary cap, where in the NBA teams can go above the cap to resign a player under the Bird rule. Of course, that doesn't make the NBA' salary cap "fixed", either.