Ramsey is slowly but surely forcing the Jaguars into considering a blockbuster trade this offseason, league sources told ESPN.
One league source said he "absolutely" believes the Jaguars will entertain the idea of trading Ramsey, while an NFL general manager said he would not be surprised if that's the route the Jaguars decide to pursue.
Jacksonville responded to the report Sunday, saying the team is not planning to trade Ramsey.
"The Jaguars have zero intention of trading CB Jalen Ramsey," the team said in a statement. "There is no truth to this rumor."
Much of the scrutiny has been brought on by Ramsey, who tweeted last week: "When I'm gone from here, y'all gone miss me."
When I'm gone from here, y'all gone miss me. I ain't even trippin lol— Jalen Ramsey (@jalenramsey) November 12, 2018
Ramsey addressed the tweet Thursday, saying it was meant for "fake fans" who haven't stuck with the Jaguars, who have been among the biggest disappointments in the NFL this season. The Jaguars went 10-6, won the AFC South and reached the conference championship game last season.
But despite starting 3-1 this season, Jacksonville (3-6) is last in the AFC South thanks to a five-game losing streak.
Ramsey emphasized Thursday that he wants "to play for one team my whole career," but his behavior has caught the attention of his team, according to sources. The outspoken cornerback has made headlines multiple times in recent years because of his brash opinions -- both about himself and opposing players.
As unthinkable as trading away a player of Ramsey's caliber would be, bear in mind that the Giants considered trading Odell Beckham Jr. last offseason before deciding to sign the star receiver to a long-term contract.
Ramsey has next season and a fifth-year option remaining on his contract with the Jaguars, who will either have to make him the highest-paid cornerback in the game or make the decision to move on from him.
ESPN's Michael DiRocco contributed to this report.