The 29-year-old, who is scheduled to make $1.5 million this season, scored twice and finished with seven points in 27 games in 2012-13. He missed the start of the season with an eye injury.
Jones scored 17 goals in 2011-12 and 18 during the 2010-11 season. He has 52 goals and 94 points in 282 games with the Oilers and Nashville Predators. The Oilers claimed him off waivers from Nashville in March 2010 and re-signed him as a free agent on July 8.
Other teams have until Thursday at noon ET to claim Jones.