Ramsey's agent, David Mulugheta, confirmed the trade request to Schefter.
The Jaguars have spoken with interested teams but there is currently no plan to deal the two-time Pro Bowler, Schefter and Mortensen report. Jacksonville is seeking at least one first-round pick and is demanding more in any potential trade, sources told Schefter.
Trade rumors have followed Ramsey since the Jaguars' disappointing 2018 season. During Sunday's game against the Houston Texans, Ramsey got into a heated verbal dispute with head coach Doug Marrone.
Ramsey's trade request stems from that confrontation and his frustration with his usage in the 0-2 Jaguars' defense, sources told NFL Network's Ian Rapoport.
The 24-year-old is widely considered the best corner in football and has been seeking a new contract reflecting that status; he even arrived at this year's training camp in a money truck. The team, however, has not budged.
Playing in the final year of his rookie deal, Ramsey will earn $13 million for the 2020 season after the Jaguars exercised the fifth-year option on his contract. Any trade for Ramsey will likely come with a new contract for the shutdown corner.
The Jaguars selected Ramsey fifth overall in the 2016 draft and he blossomed into a first-team All-Pro in his second season.