Multiple media organizations are reporting that Murray has an agreement in place that will see him sign a five-year contract for $42 million US with $21 million US of that guaranteed by the Eagles.
The 27-year-old free-agent is visiting with Eagles management and if all goes well the contract is expected to be signed soon.
Philadelphia has been in the market for a new running back since trading LeSean McCoy to the Bills last week.
Murray, the NFL's leading rusher last season, played for the Dallas Cowboys since he began his NFL career in 2011. He tied the Seahawks' Marshawn Lynch for the most rushing touchdowns last season with 13. He turned down an offer from the Cowboys last fall for a four-year deal worth $16 million US.
Last season was Murray first full season as he had missed games in each of his first three years as a pro due to injury. Injuries are something the running back knows about as he finished the final four games of last season playing with a broken left hand. He broke that hand in a game against the Eagles.
Murray has been to the Pro Bowl the last two seasons. In 2013, he rushed for 1,121 yards recording 9 touchdowns and received 1 touchdown. He followed that up in 2014 by rushing for 1, 845 yards.