And England keeper Hart is in the frame to step in after his loan to West Ham ends.
The Premier League champions are willing to make Courtois the best keeper in the world with a deal worth £200,000-a-week including add-ons.
But fresh terms have not been thrashed out and that has left the door open for Real to make a massive bid in the summer.
Hart, meanwhile, lost his place to Adrian under David Moyes but is still expected to trigger interest when his loan ends in the summer.
He has a year left on his contract but City will not stand in his way if he wants to leave the Etihad.