The French sensation has been heavily linked with a number of clubs, and his compatriot claims the Spanish side should sign him this summer
Real Madrid should sign Kylian Mbappe and then loan him back to Monaco for the benefit of his development, according to Franck Leboeuf, who thinks the forward could become "the new Ronaldo".
Ex-France defender Leboeuf believes Les Bleus' new star would be best served by spending another season with Monaco, but understands the Ligue 1 champions would struggle to resist a world-record offer for the 18-year-old.
Lebouef therefore believes a sign and loan strategy from Madrid could be the best solution after Mbappe discussed the European champions' interest in him this week.
"He seems to be able to handle everything and able to become, I don't know, maybe the new Ronaldo," Leboeuf said to ESPN.
"It is very complicated because he is not the only one to decide [his future]. Monaco have something to do with it.
"If you offer £100 million or £130m to come to Real Madrid it is hard for Monaco to say no, but if we only talk about the football I wish him to stay in Monaco for another year to be able to handle more of his football under pressure.
"He only played for six months - don't forget he didn't start the season, he only started in November. He is very young and very inexperienced even if he shows the opposite.
"He has to be patient, his time [to move] will come. Obviously we don't wish him to get injured but if he carries on like that there is no way he is not going to have a fantastic career.
"Being under Leonardo Jardim in Monaco with all the players that he knows, and with a certain way of life in Monaco with no pressure, he can become even bigger and maybe go to Real Madrid.
"Maybe Real Madrid can sign him from Monaco and loan him for a year to Monaco, that could be the best way."
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Leboeuf is extremely impressed with Mbappe's maturity after he won his fourth France cap in the 3-2 victory over England at Stade de France, setting up Ousmane Dembele's winner.
"He has everything," Leboeuf said. "He's not 20 yet and already mature, he is a very smart person on top of being a fantastic football player.
"He has that little plus which makes players exceptional and he's very humble. When he talks to the press you see somebody who already seems to be already 30.
"He has the pace, he has the technique, he seems to have the physique to carry on all season long and be effective.
"He's really exceptional, he has everything. Now, how is he going to cope with the fame? I don't know.
"His feet seem to be on earth, but I don't know what's going to happen in the future, his close future, whether he's going to stay in Monaco or go maybe to Real Madrid or somewhere else."