The 31-year-old's current deal with the Gelsenkirchen side runs until the summer of 2014, and Jones has already stated more than once that he wants to end his career in MLS.
Nevertheless, Schalke has no intention of losing Jones any time soon and is willing to offer the midfielder a two-year extension to his current contract.
The Konigsblauen are hopeful that Jones will commit his future to the club, although his wage demands could prove to be a serious obstacle. The midfielder is currently one of S07's top earners, and the Bundesliga side is reluctant to offer him a pay increase.
Jones joined Schalke from Eintracht Frankfurt in the summer of 2007, and has since made over 100 Bundesliga appearances for the Veltins Arena outfit.