Adams told Manish Mehta of the New York Daily News:
"I don't feel like he's the right leader for this organization to reach the Promised Land. As a leader, what really bothers me is that he doesn't have a relationship with everybody in the building.
"At the end of the day, he doesn't address the team. If there's a problem in the locker room, he lets another coach address the team. If we're playing sh---y and we're losing, he doesn't address the entire team as a group at halftime. He'll walk out of the locker room and let another coach handle it."
Adams' comments come after he requested a trade from the organization earlier in the offseason.
In June, Gase said he was hopeful the sides could reach an agreement to avoid losing one of their defensive cornerstones.
"Yes, I want Jamal on our team," he told reporters.
Gase, who led the Jets to a 7-9 record during his first season in charge last year, also praised the All-Pro safety's work ethic.
"His play speed is phenomenal, both in practice and on game day," he said.
Those remarks fly in the face of Adams' characterization of his discussions with the organization in recent months, though.
The 24-year-old Texas native said the front office questioned his desire during a May conversation and wanted to "monitor" whether he was "all-in with the Jets and all-in with football," which played a role in his decision to request a trade, per Mehta.
"It was very insulting," Adams said. "You know I bust my ass for that organization every day. I work my ass off. For them to say that to me, I was like 'OK ... Whoa! That was little bit too far.'"
The LSU product, who's earned two straight Pro Bowl selections, said the entire situation has taken a toll on him with the 2020 season set to kick off in seven weeks.
"My happiness is way more important than the rest of this," Adams told Mehta. "I can't deal with all that anymore. It's draining."
The standout defender recorded 75 total tackles, seven passes defended, 6.5 sacks, two forced fumbles and an interception to earn a strong 87.9 overall grade from Pro Football Focus in 2019.
He confirmed to the New York Daily News he's not planning to hold out if the Jets can't find a trade.
They're scheduled to open the regular season Sept. 13 with a road game against the AFC East rival Buffalo Bills.