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.
It's cool when you think about how many great American players have played the game and the two players that were at that 18-game point streak and what they've done in their careers. It's pretty cool right now, but it was kind of overshadowed by the loss.
— Blackhawks forward Patrick Kane after breaking the record for longest point streak by an American-born player with a goal and an assist in a 3-2 overtime loss against the Kings