The Jaguars placed the franchise tag on the pass-rusher, which could be worth $17.8 million in 2020 on the one-year tender, but the two sides have until Wednesday's deadline to agree on a long-term deal.
As Jeremy Fowler of ESPN reported earlier this month, Ngakoue has asked for a trade and doesn't plan to sign the franchise tender or report to training camp.
Ngakoue notably argued with Tony Khan, the team's senior vice president of football administration and technology and son of owner Shad Khan, on social media while calling for a trade before the draft.
However, general manager Dave Caldwell said at the time he didn't generate much interest.
"Truth be told, we exercised the franchise tender. We weren't able to get a trade. Actually, weren't even really able to get an offer," Caldwell said, per Mike Garafolo of NFL Network. "So, I think his options are very limited at this point in time. We'll welcome him back with open arms when he's ready to come back, and we look forward to it."
Renewed interest could allow a trade to take place, with Rapoport noting it would be "complicated...but not impossible."
The 25-year-old has been one of the top pass-rushers in the NFL over the past four years, totaling 37.5 sacks in 63 games. He also has 14 career forced fumbles, including a league-leading six in 2017 to earn his lone Pro Bowl selection.
Ngakoue set a personal high with 41 tackles in 2019 to go with his eight sacks, adding an interception returned for a touchdown.
If he is traded, Jacksonville will try to move forward with recent first-round picks Taven Bryan, Josh Allen and K'Lavon Chaisson to carry the pass rush.