The two sides have had multiple conversations since the NFL draft, but the Jets told him they prefer to wait on a long-term extension and Adams wants a deal before the season, sources said.
The Adams camp is upset, claiming the Jets are dragging their feet, sources said.
On Wednesday, the possibility of a trade came up in a conversation between the two sides, sources said, but there are conflicting accounts on how serious those talks were.
The Jets remain intent on signing Adams, 24, to an extension and have no desire to trade him, a source said. Adams is said to be open to a trade if his contract demands aren't met. More than half the teams in the league have reached out to the Jets to express interest, according to a source.
Clearly there is a fundamental difference on the timing of a potential extension. They haven't discussed money yet, sources said.
Adams, eligible for a new contract now that he has completed his third season, said in January that he wants an extension by the start of the 2020 season. He is due to make $3.5 million this year. His salary jumps to $9.9 million in 2021, the amount of his fifth-year option.
Conversely, the Jets don't feel there is a sense of urgency because they have Adams under team control for at least two years and have the option of the franchise tag in 2022. Another component is the uncertainty created by the coronavirus pandemic, which could have a massive impact on NFL revenue.
Since 2011, only 16 of 223 first-round picks received a new contract after their third season. The most recent was Carolina Panthers running back Christian McCaffrey, who was drafted eighth overall in 2017 -- two spots after Adams.
Adams believes he is worthy of being an exception after being named All-Pro and making two Pro Bowls in his first three seasons. He hasn't named his price publicly, but it's believed he wants to become the NFL's highest-paid safety. The Chicago Bears' Eddie Jackson has the highest average per year at $14.6 million.
The Jets entertained trade offers for Adams last fall at the trade deadline, with the Dallas Cowboys showing interest. Adams was furious upon hearing his name had come up in trade discussions.
General manager Joe Douglas said in February that his goal was to make Adams "a Jet for life," and he hasn't wavered on that position publicly. After the draft, Douglas said his plan was to reach out to Adams' agent to initiate contract talks. He did, but those talks haven't been fruitful.
In the meantime, Adams is skipping the voluntary virtual offseason.
Longtime NFL reporter Gary Myers first reported on the stalemate via Twitter.