The 23-year-old holding player won many plaudits for his performances in Germany's run to the World Cup semi-finals this summer, which has attracted the interest of some of the top clubs in Europe.
Chelsea manager Carlo Ancelotti has been linked with a move for the 23-year-old as a replacement for Michael Ballack, who Khedira replaced in the German starting lineup after Ballack was injured in the FA Cup final prior to the tournament.
Ancelotti is thought to be keen on Khedira replacing Ballack at club level too, with Joe Cole also departing Stamford Bridge for Liverpool.
Meanwhile Old Trafford chief Sir Alex Ferguson will soon be in the hunt for replacements for veteran pair Paul Scholes and Ryan Giggs in the Red Devils' midfield, and may be persuaded to lodge a bid for the highly rated German with fellow midfielders Owen Hargreaves and Anderson sidelined.
The Spanish media had reported that an £8.5 million move to the Bernabeu was imminent. However, Khedira has admitted that he is flattered to be linked with Los Galaticos but quashed claims that he had already put pen to paper.
"There is no agreement and there is also no decision on my future," he explained to German magazine Kicker. "I am delighted about such a club being interested in my services, but first of all I need to think things over.
"I was having a very fairly and square chat with Christian Gross and he was very firm on telling me how he would like to carry on working with me in the future.
"This was impressive. For now I am going on holiday and afterwards I am going to get back on the table discussing the future."
Only last week Stuttgart director Jochen Schneider moved to calm speculation that the Stuttgart starlet was to be sold but now Schneider seems to have had a change of heart.
With Khedira entering the final year of his contract, the Stuttgart chief has opened the door on a move now rather than risk losing him for nothing next summer.
"Months ago we have tried to thrash out a contract extension with Sami but we did not succeed," Schneider said. "And now Real Madrid has officially indicated their interest in him. We shall see."
By James Martini
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
