Per ESPN's Rich Cimini, the Jets have "no interest" in signing the three-time Pro Bowler.
Clowney is the biggest remaining free agent on the market, though there is no indication a signing is imminent.
Per Yahoo Sports' Charles Robinson, "several NFL sources" believe Clowney won't sign soon.
A source told Robinson that Clowney "may be inclined" to do what he did last year when he didn't report to camp with the Houston Texans until August. The Texans traded Clowney to the Seahawks on Sept. 1 for Jacob Martin, Barkevious Mingo and a 2020 third-round pick.
Clowney did have core muscle surgery in February after playing through the injury during the 2019 season. The South Carolina alum told Mark Berman of Fox 26 in May that he will "ready to go whenever the time comes."
Drafted No. 1 overall by the Texans in 2014, Clowney was named to three straight Pro Bowls from 2016-18, which included registering 18.5 sacks over those last two seasons. The 27-year-old had 31 combined tackles, 13 tackles for loss and three sacks in 13 games with the Seahawks last season.