The 18-year-old has become one of the most in-demand players in world football after a sensational breakout season for the Ligue 1 champions.
Real, Arsenal, Manchester United, City and PSG have all been linked with transfer moves for the talented teenager, with bids up to and around €130 million believed to have been made.
But now Marca, a notoriously Real centric paper, have claimed that Mbappe will only consider signing for the Spanish champions.
The only dilemma remaining for the French starlet is whether he signs for Real this summer or next.
It had been suggested that Real could loan Mbappe back to Monaco, though recent revelations over Cristiano Ronaldo could affect that.
The Portuguese winger is thought to be furious with his treatment over recent tax scandal allegations and has told the club he wants to leave Spain.
If Ronaldo does depart, that will leave a big void in the squad and increases Real’s need to sign Mbappe this summer and begin integrating him in the squad.
Mbappe scored 15 goals in Ligue 1 last season in a remarkable season, also becoming the youngest ever scorer in a Champions League final.
Arsene Wenger had hoped to persuade him to join Arsenal, believing his support of the club as a child and the offer of being the club’s main man could swing a deal.
But Ronaldo’s potential departure would surely create an opportunity to replace the five-time Ballon d’Or winner that is too alluring to turn down, while recent events have hastened Real’s desire to conclude a deal.