Ian Rapoport of the NFL Network reported that the Cowboys likely won't even consider it until the team has a long-term extension with quarterback Dak Prescott in place:
"From my understanding, there's really nothing there from the Cowboys' perspective. First of all, they would need to take care of Dak Prescott first, their franchise quarterback. Not gonna come in and sign another player to a huge deal before Dak, that's not going to happen. If they eventually did an extension for Dak, maybe in July, maybe potentially they could consider something, but I see nothing imminent right now."
There was major buzz before the 2019 NFL trade deadline that Adams was on the trade block, with the Cowboys coming up as one of the teams reportedly in the running to land him:
That didn't come to fruition, however, and Adams wasn't happy to hear his name in trade rumors:
Adams' future in New York is uncertain. ESPN's Adam Schefter reported on April 17 that the star safety wasn't expected to participate in the team's virtual, voluntary offseason program, though general manager Joe Douglas told reporters on April 20 that there hadn't been trade talks at that time and that the goal was to "keep Jamal here for a long time."
The NFL Network's Mike Garafolo reported last week that the team does plan to sign him to a long-term extension, though longtime sportswriter Gary Myers previously reported that the divide between the team and player was growing:
Gary Myers @GaryMyersNY
The divide between the Jets and Adams escalated in last few days and this has potential to get ugly. It’s not even about the dollars right now. Jets want to wait at least until regular season to consider new deal. Adams wants it now. Pay me or trade me? Could be getting there. https://t.co/LDmt8VKLUP
So it remains to be seen if Adams will indeed remain in New York for the long haul. He's emerged as one of the best safeties in football, with two Pro Bowl appearances and a first-team All-Pro selection in 2019. Sam Monson of Pro Football Focus ranked him as the 32nd best player in the NFL last season, citing his versatility and unique ability to rush the passer effectively.
Keeping him, then, makes the most sense for the Jets. It seems likely that he'll get a long-term extension at some point, though it may not come as quickly as he'd prefer.