The Manchester City ace is stumbling over a new contract and Los Blancos are reportedly monitoring the situation
According to ESPN, the La Liga giants are weighing up a move for the forward as Sterling enters the final two years of his contract.
In the past the England international has admitted he is open to a move abroad at some stage of his career.
Betfair see a move to the Bernabeu in January as unlikely at 16/1, with City being reluctant to lose a key player midway through the season.
But the odds of a summer move to Madrid are much shorter as there continues to be no sign of him putting pen to paper on a new deal.
The 23-year-old has had a flying start to the season with four goals and three assists for club and country.
Betfair Spokesperson Katie Baylis said: “With reports that Real Madrid are keeping an eye on Sterling’s situation at City, we now have odds on Sterling heading to the Bernabeu at 16/1 in the next transfer window as City are more than likely to try and keep him.
"However those odds shorten to 7/2 for him to head to Real at the end of the season and it could be one of those wait and see situations ahead of us.”
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