The Spanish giants are likely to dispense with the Dutchman this summer, especially after completing the signing of Cristiano Ronaldo from Manchester United.
Sneijder, however, reiterated that he has no intention of leaving the Bernabeu, saying he's ready to fight for a regular spot.
"I'd like to stay and hope coach Manuel Pellegrini will give me a chance but there are many rumours," he said.
Sneijder fell down the pecking order at Real last season, and his chances of playing regularly have become more negligible since the arrival of Portugal ace Ronaldo.
Real want to run the rule over more high-profile players this summer, which will diminish Sneijder's prospects much further.
Chelsea are reportedly eager to bring in the 25-year-old, after failing to sign Franck Ribery and Alexandre Pato.
Sneijder joined Real two years ago from Ajax for €27 million, but the Blues are expected to offer the unsettled player a much lower fee.
Sneijder’s highlights
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