The Sun says Real were already planning a summer swoop for City's England winger before the FFP bombshell.
Now they feel a lack of European football can finally see Sterling head to the Bernabeu.
The forward, 25, is under contract for another three years.
He earns around £300,000 a week, though in November talks began over increasing his salary to £450,000 a week.
Yet City face missing out on a £170m Champions League jackpot if their appeal fails. And without that income, they could not boost his wages.
Sterling has made no secret of the fact he would love to play abroad at some stage in his career.