Jones-Drew let the Raiders know Thursday night that he wanted to play in Oakland. It's his hometown team and his permanent residence, and he would have better potential to start with the Raiders.
Jones-Drew, 29, needs to pass his physical and finalize a contract, but the two sides are now "close" to a deal, another source told ESPN.
In Oakland, Jones-Drew should challenge oft-injured Darren McFadden for the starting job. The fourth overall pick in 2008, McFadden never has played an entire season and missed three games in 2013.
Jones-Drew was a first-team All-Pro in 2011 after leading the league with 1,606 yards rushing. He played for current Raiders offensive coordinator Greg Olson when Olson was the Jaguars' assistant head coach/quarterbacks coach in 2012.
Slowed by a foot injury, Jones-Drew averaged just 3.4 yards per carry and rushed for 803 yards and five touchdowns in 15 games last season. He also missed 10 games in 2005 because of a foot injury.
Information from ESPN.com's Paul Gutierrez was used in this report.