The 27-year-old has suffered a number of injury problems this season and is thought not to feature in Carlo Ancelotti's plans for the future.
Khedira will be available on a free transfer when his contract ends this summer and Tonnies says that Schalke are hoping to persuade the World Cup winner to move to Gelsenkirchen.
“There have been initial talks. We believe that a fit-again Khedira would help us,” Tonnies told Bild.
Khedira’s contract expires on June 30, meaning he has been free to discuss a contract with other clubs since the end of January.
Reports in Spain suggest the former Stuttgart star has already agreed a move to Germany but won’t reveal his decision until the end of the season.
It has also been suggested that Kevin Prince-Boateng will be forced to make way in order to free up capital for the Khedira deal.
The Germany international, who has made just three Liga starts for Madrid this season, is also reported to have attracted interest from Borussia Dortmund, Arsenal and Chelsea.