But Arsene Wenger and Gunners chief Ivan Gazidis were spotted in Nice, just 13 miles from Monaco, on Monday.
And Manchester United – fresh from qualifying for next season’s Champions League – are also in the race, although they fear he has already set his heart on Madrid.
The teenager is a huge fan of Real boss and fellow Frenchman Zinedine Zidane, putting them in a strong position.
And they can also offer the prospect of playing with childhood hero Cristiano Ronaldo.
But the youngster is also intent on continuing his progress and he is likely to be used sparingly in the Spanish capital with Ron, Karim Benzema and Gareth Bale ahead of him.
Mbappe’s dad is the man in charge of his son’s professional future and he is now courting bids from all over Europe from his son who is destined to become the world’s most expensive player aged just 18.
Wenger revealed in March: “Well, I approached him last year because I really believe that he has an exceptional future ahead of him, that he has all the qualities.
“He reminds me of a young Thierry Henry with the same clever look about him, the same qualities of intelligence in his movements and cat-like finishing. So that’s why.
“I think he’s an exceptional talent who promises to have a great future.”
“The player would tell you that I was at his home last year to try to get him here.
“Because he was at the end of his contract but Monaco managed to keep him and the decision was very, very tight.
“But I could understand it as well because he was educated there and at the end decided to stay there.”
Arsenal have reportedly already bid £87m for Kylian Mbappe