"He's going to be here. Those [stories] are false," coach Adam Gase said Wednesday. "I talked to Quinnen. I have not heard one thing from anybody in the front office about him being traded. ... There's nothing to that. It's false."
General manager Joe Douglas also spoke to Williams and his agent to put to rest the rumors. The NFL trade deadline is 4 p.m. ET Tuesday.
Williams has attracted interest, as he did at last year's trade deadline, but the Jets (0-7) -- the NFL's only winless team -- view him as a piece to their foundation.
The Jets have made two recent trades, dealing nose tackle Steve McLendon and linebacker Jordan Willis, fueling the perception they are in fire-sale mode. Douglas isn't averse to trading big names, as he dealt star safety Jamal Adams before training camp, but that involved a contract dispute.
Williams' contract isn't an issue. He has two years remaining on his rookie contract, plus a fifth-year option, and isn't eligible for a new deal until after the 2021 season.
The 22-year-old Williams hasn't lived up to draft expectations but has elevated his play this season. He leads the team with three sacks and is coming off a strong performance against the Buffalo Bills.
The Jets like his upside, although they want to see more consistency.
"There have been some times where I really see him show up," Gase said. "It's the consistency of down in and down out, max effort, playmaking ability, finishing the plays and doing the right thing, not having roughing-the-passer penalties. That's the maturation of a young player."
Williams has been flagged three times for roughing the passer and once for a face mask, which proved costly in a loss to the Denver Broncos.
"Honestly I just don't read it, man," Williams told SiriusXM radio of the trade rumors. "Just don't look at it, just don't read it. You just don't really listen to it, just don't really pay it any attention, man."