An unnamed NFC team reportedly offered a 2020 first-rounder and a 2021 fifth-rounder for Ramsey, while an unnamed AFC squad proposed sending a 2020 first-rounder and a player in exchange for the defensive back, sources told ESPN's Dianna Russini.
Ramsey said on a podcast over the summer that he'd like to play for his hometown Tennessee Titans, or the Raiders once they get to Las Vegas, if he doesn't remain in Jacksonville after the end of his current deal.
The two-time Pro Bowler spoke with the media Tuesday but declined to directly address his trade request, which was confirmed by his agent Monday.
However, he denied previous reports that the request was the result of his Week 2 altercation with head coach Doug Marrone.
Ramsey is in his fourth season with Jacksonville. He's recorded the fifth-most deflected passes (45) in the league during his tenure while also securing nine interceptions and a first-team All-Pro nod in 2017.
The Jaguars have been dismal since losing the 2017 AFC Championship Game. They finished 5-11 a year ago and started this season 0-2.