The Jaguars are looking to reach agreements on trades that can be processed when the league year opens March 13.
Hyde was traded to the Jaguars by the Cleveland Browns last season, and he rushed for 189 yards on 58 carries in eight games with Jacksonville.
Jackson has been in Jacksonville since 2016 after signing a six-year contract worth up to $90 million. He has totaled 18 sacks over the past three seasons.
The Jaguars will attempt to recoup some value for the two players, as both had been expected to be leaving Jacksonville this offseason.
Information from ESPN's Mike DiRocco was used in this report.