According to German newspaper Bild, the 26-year-old has caught the eye of scouts from Premier League champions United.
Jones' agent Roger Wittmann did not confirm there have been any offers for the player, but admits talks are due to be held to assess his plans for next season.
"It is true that Jones enjoys a good reputation in England," Wittmann told Bild.
"I will be meeting with Jermaine and we will be discussing everything: last season, the national team and all the speculation that there has been.
"If I hear that Jermaine is interested in England then we will have to have a serious talk with Schalke about it."