The People says Rooney has been plunged into despair by revelations about his private life and Real chief Joe Mourinho is ready to offer him an escape next summer if he decides he fancies a fresh start abroad.
Such a move is certain to infuriate Mourinho's good friend Sir Alex Ferguson, who will fight tooth and nail to hang on to his star man.
But that is unlikely to prevent a bid from the Portuguese, who is a confessed admirer of Rooney.
Mourinho has already spoken of his desire to work with the player, but told Ferguson he could "rest easy" as a move for the player would be "impossible".
However, that was before Rooney's dirty linen was aired in public and Real president Florentino Perez is determined to let the hitman know there is an exit route to Spain if he needs one.
Sources in Spain said: "A move for Rooney is not impossible.