With Arsenal and a host of other big clubs interested, Mbappe has set his hearts on Real Madrid.
Mbappe enjoyed a breakthrough season with Monaco which saw him score 26 goals in all competition as they won the Ligue 1 title and had an impressive run to the semi-final stage of the Champions League.
The 18-year-old has become the toast of European football with several clubs said to be interested.
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According to reports, Monaco have already turned down world record transfer offers from Real Madrid and Arsenal.
Spanish newspaper Marca are now reporting that the France international has told Monaco that he wants to join Real Madrid.
Real Madrid are on the verge of tabling an improved bid for the striker.
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The Spanish and European champions are now keen to quickly sigh the youngster following concerns over the future of Cristiano Ronaldo.
They were shocked last week when Ronaldo informed them that he will be leaving this summer following the tax evasion allegations brought up against him by prosecutors in Spain.
Mbappe is also a huge target of Real Madrid president Florentino Perez who wants to make a statement with the signing of the youngster after his re-election.