The USA international will not fly out to Qatar with his team-mates on Friday, but instead remain in Gelsenkirchen, awaiting offers to leave the club.
He has been granted permission to do so by the club's director of sport Horst Heldt, who believes it is better for the 32-year-old to be in Germany "in case something could change" in his situation and to enable him to "assess eventual offers".
Jones' contract expires in the summer and, after being dropped earlier on this season, he has seen his opportunities limited this year.
The chances of Schalke extending his contract beyond the summer appear slim and it appears he is now keen on leaving even before his contract expires.
He will be left behind in Gelsenkirchen with Klaas-Jan Huntelaar, who is continuing his recovery from a serious knee injury.