Murray's agency confirms to Action News that his agent, Bill Johnson, is in the process of orchestrating terms that will get Murray to the Titans.
Former Eagles head coach Chip Kelly lured Murray away from division rival the Dallas Cowboys before the start of the 2015 season with a five-year contract worth $42 million, with $21 million guaranteed.
It remains unclear what the Eagles will get in return for Murray.
Murray is a two-time Pro Bowler.
An earlier report from The Associated Press cited sources saying Eagles Cornerback Byron Maxwell and linebacker Kiko Alonso are being sent to the Miami Dolphins. That trade will reportedly give the Eagles a draft choice.
Both deals won't be announced until Wednesday, the first day of free agency.
The deal is pending physicals, and Alonso has knee issues.
All three had a disappointing year in Philadelphia after they were acquired before the 2015 season by coach Chip Kelly, who was fired before the season finale. Philadelphia finished 7-9.