Law narrowed his choices to teams that offered direct links to their coaching staffs: the Jets, Patriots and Cleveland Browns. He has played for Eric Mangini, Bill Belichick and Romeo Crennel.
"Yeah, I talked to them a few times, and it was pretty close," Law told reporters at the Jets' facility in Florham Park, N.J. "It's always going to be a relationship there with the Patriots organization and the fans. I chose to come here to New York, but I've always loved the Patriots.
"I'm a Jet right now, and we got to play against them. So right now, they've got to be the enemy."
Nobody is sure what Law's role will be in Thursday night's game against the Patriots, but NFL Network analyst Steve Mariucci predicted if Law plays with a short week of prep time the snaps will be limited.
"If he's been sitting on the couch he's not going to be ready to play, but if you know Ty Law he's probably in very good shape and been training all along and waiting for this opportunity," Mariucci said on a conference call.
"Just coincidentally it's against his former team. That's an interesting move. I'm anxious to see if he has any participation in the game with such short preparation time, but good acquisition. He's 34, in Brett Favre's generation and he still has some football left.
"When he plays, whether it's this game or next game, I'm sure he'll have a role. I doubt if it'll be an every-down spot. It'll probably be nickel situations at first and then see how he feels and work him in gradually that way."