Chelsea boss Carlo Ancelotti is believed to be in the hunt for the playmaker after releasing Joe Cole, Michael Ballack and Deco in the close season.
Khedira has enjoyed an impressive World Cup finals and his performances have also courted the interest of Manchester United.
Sir Alex Ferguson is said to be eyeing the player as a replacement for 35-year-old Paul Scholes in the Old Trafford midfield engine room.
Stuttgart could be lose their man on a free next year when his contract expires and the German outfit are believed to be willing to deal at £12million for Khedira's services.
Gross says the prospect his lynchpin helping Joachim Low's team to glory in South Africa could see the big clubs swoop to land his services.
The former Tottenham chief told The Sun: "It would be very painful if Sami left on a free. If he has two more great World Cup games, all the big clubs will come for him."