The Blancos have made a major effort to land the star forward, but his current club are so far not budging.Paris Saint-Germain are yet to respond after Real Madrid offered €220 million (£189m/$260m) for Kylian Mbappe, sources have confirmed to Goal.
Madrid have been making a strong push to land the 22-year-old superstar, whose contract with PSG will expire at the end of the current season.
But talks between the clubs have stalled, making it likely that Mbappe spends the remainder of the campaign in the French capital.
Los Blancos have already had two bids rejected by PSG for Mbappe, the most recent of which was worth €170 million (£146m/$200m), plus €10m (£9m/$12m) in add-ons.
PSG have been doing everything in their power to keep Mbappe at Parc des Princes, but the forward has turned down no fewer than six contract renewal offers.
The Ligue 1 outfit could see Mbappe leave for free at the end of the season, but have so far indicated they won't be swayed by any big-money bids this transfer window.
Mbappe, who has made it clear he wants to join Madrid, can sign a pre-contract agreement with the Blancos as soon as January to join them on a free transfer next summer.