Umenyiora, 33, did not name the club, but said he turned it down because it wasn't an offer from the Giants -- the only team he wanted to close his career with.
NFL Media can confirm the Jets were the team that contacted Umenyiora, according to a source who has spoken to the former Giant.
So it goes for the pass rusher, who will finish 49th all-time in sacks with 85, just ahead of Raiders legend Howie Long.
Umenyiora's farewell news conference provided some clarity into his relationship with the Giants and general manager Jerry Reese -- a relationship many believed was contentious. The two had some legendary battles over Umenyiora's contract, but both the general manager and Umenyiora said they maintained a close bond all along.
"People were saying he and I were feuding, and we would be at the Tick-Tock diner on Route 3 (in Clifton, N.J.) having breakfast together," Reese said this week in a statement released by the team. "I said, 'Let's just meet and have breakfast and talk.' He said, 'Okay.' We went out and had breakfast and talked about everything that was going on. More than anything else, we laughed about how everybody was saying that we hate each other."
Umenyiora added, "For past three weeks, I've been in negotiations with Jerry Reese. I wanted a two-day contract."
The funny thing about Umenyiora's retirement and insistence on only playing for the Giants is that the team could absolutely use him right now given all the uncertainty across their defensive line. With the return of defensive coordinator Steve Spagnuolo, he would already know the system.
Maybe Reese should consider that two-day deal after all.