The Germany international has suggested that he is likely to depart the Santiago Bernabeu but pointed out that anything could happen before August 31
The Germany international has just one year left on his current contract with the European champions and Blancos boss Carlo Ancelotti revealed on Friday that the midfielder had turned down an extension.
Goal understands Chelsea had edged ahead of Arsenal in the race with the midfielder's wage demands derailing a potential move to the Emirates.
However, Khedira has also been linked with clubs such as Bayern Munich, Fiorentina and Napoli, but while the 27-year-old hinted that he is edging towards the exit door at the Santiago Bernabeu, he says that he could still end up staying in the Spanish capital.
"Right now I'm a little out of Real Madrid," he is quoted as saying by Bild. "But until August 31 anything is possible."
Khedira, who was left out of the squad for Friday's Supercopa de Espana second-leg clash with Atletico Madrid, joined Real from Stuttgart in the summer of 2010.