That's despite an April 1 report from ESPN's Dianna Russini stating that Clowney dropped his asking price from $20 million to the $17 million-$18 million range.
ESPN's Jeremy Fowler also reported on April 9 that Clowney could also be considering "shorter-term deals."
There isn't a shortage of potential options for Clowney, a three-time Pro Bowler with 32 sacks and 80 quarterback hits in 75 regular-season games.
The question is whether a team is willing to pay Clowney's price, which hasn't occurred yet as the NFL draft came to an end Saturday.
Here's a look at four teams who could potentially land the ex-South Carolina star.
Adding Clowney would give the Cleveland Browns one of the NFL's most dominant defensive lines, which is currently led by Myles Garrett (10 sacks in just 10 games last season).
Lining Clowney and Garrett on opposite ends of the line would create a serious problem for opposing offenses, but the question is whether the Browns have interest.
Browns general manager Andrew Berry declined comment (h/t Mary Kay Cabot of Cleveland.com) on whether the team had an interest in Clowney, but Fowler reported on April 4 that the team had interest at one time.
"Cleveland Browns have shown interest in Jadeveon Clowney, and some people around league believe Cleveland got closer with Clowney than other suitors, though nothing ultimately happened from recent talks. Seattle's offer hasn't been what Clowney wants," Fowler tweeted.
Cleveland has made a concerted effort to improve its defense through the draft, with the Browns selecting safety Grant Delpit, interior defensive lineman Jordan Elliott and linebacker Jacob Phillips with their Day 2 picks.
Clowney could be the final piece to the puzzle as the Browns look to make the playoffs for the first time in 18 years.
The Colts' front seven is already terrifying with Darius Leonard and DeForest Buckner leading the way, but the team would be the unquestioned AFC South favorite with Clowney in the mix.
The six-year veteran would line up opposite Justin Houston and put the promising Kemoko Turay into a backup role, creating one of the deepest pass-rushing units in the league.
Jeff Kerr of CBS Sports explained why the Colts could be a good fit on April 9:
"The Colts are closer to contention than the Giants are, especially after signing Philip Rivers. Clowney is very familiar with the division, having spent the first five seasons of his career with the Houston Texans. Indianapolis would be an enticing destination for Clowney, especially since he'll get the opportunity to line up opposite of Justin Houston (who finished with 11 sacks last year)."
Indianapolis' window to win is right now. The Colts added quarterback Philip Rivers on a one-year deal and picked up two highly productive skill-position players in USC wideout Michael Pittman Jr. and Wisconsin running back Jonathan Taylor.
The future might lie in the future development of fourth-round draft pick Jacob Eason, a quarterback out of Wisconsin, but Clowney is just 26 years old and could be a big piece of this defense for years.
The Tennessee Titans have undergone an overhaul of their defensive line, trading Jurrell Casey and letting Austin Johnson walk in free agency.
Jeffrey Simmons, the team's first-round pick in 2019, figures to be the cornerstone on the defensive line now. But adding Clowney can only help the Titans stomp the bevy of potent passing and rushing attacks found in the AFC, led by the Baltimore Ravens and Kansas City Chiefs.
Russini also told 710 ESPN Seattle's Danny and Gallant (h/t Brandon Gustafson of MyNorthwest) that she believed the Titans would ultimately be Clowney's landing spot last Tuesday.
"The closer we've been getting to the draft, the more I'm feeling like Seattle's just not into it as much," she said. "John Robinson down in Nashville, he spoke about (potentially signing Clowney) yesterday actually, and just said 'we're going to wait for this draft to go through, see how it shakes out, see what we can get and maybe we'll pick him up (after the draft).' The Tennessee Titans are still interested, (and) I think if you were to ask me where I predict he winds up, it'd probably be Tennessee."
Ultimately, the same thing can be said about the Titans as it can about any other AFC team: Defensive players should be at a premium in the conference, considering that the Ravens' Lamar Jackson and the Chiefs' Patrick Mahomes look set to dominate for 10-plus years a la Peyton Manning and Tom Brady
Teams are going to need to find a way to stop them, and players like Clowney can only help the cause.
With the Titans coming so close to the mountaintop last year following an AFC Championship Game appearance, acquiring a player like Clowney could be the addition they need to reach the Super Bowl.
Seahawks general manager John Schneider told reporters (h/t ESPN's Brady Henderson) that he wouldn't rule out a return for Clowney, who played with the 'Hawks in 2019 following the team's preseason deal with the Houston Texans.
For now, Seattle is moving forward as if Clowney isn't part of its plans. The 'Hawks have added numerous players to their front seven in hopes of applying more pressure on the quarterback, including draft picks Jordyn Brooks and Darrell Taylor and free agent Benson Mayowa.
Still, Clowney would be a welcome addition to a team that could still use more resources. Although he didn't post gaudy pass-rushing stats last year, he was still effective against the run and helped a defense that stepped up when it counted en route to an 11-5 year that ended in the playoffs.
Furthermore, Clowney made some huge plays, returning two turnovers for touchdowns (including one against the NFC champion San Francisco 49ers in a 27-24 overtime win).
Ultimately, a return to Seattle shouldn't be ruled out.