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 not just going to happen on its own. We have to have guys commit to the areas we need to improve on. We're going to be better than last year but there is still a long way to go. But I really like the pieces and where we're headed.
— Sabres forward Tyler Ennis on the progress of Buffalo's rebuilding process