The Spanish giants had a couple of bids knocked back for the prolific striker in the summer, the second of those - tabled late in the window - worth around €160m (£137m).
Mbappe recently admitted he asked to leave PSG, but the Ligue 1 side remained firm and now risk losing the France international on a free transfer next year.
Instead, it is claimed that Los Blancos will wait until June when Mbappe officially becomes a free agent, even though they run the risk of another side pouncing.
Mbappe has six goals and nine assists from 15 games in all competitions for PSG this term. body check tags ::