Mbappe has been the most talked about footballer in the transfer window with Madrid, Arsenal and Paris Saint Germain all interested in signing him.
Last he scored 21 goals as Monaco won the Ligue 1 title ahead of PSG and reached the semi-finals of the Champions League.
But Monaco have been confident of keeping hold of the 18-year-old with clubs facing the prospect of paying a world record fee for him.
And Mbappe won't have endeared himself Madrid supporters, judging by Spanish newspaper Marca.
It looks like he will stay at Monaco
Arsene Wenger on Kylian Mbappe
The report says a young fan with a Real Madrid shirt approached Mbappe and asked if he would sign but the Monaco star refused to do so and even declined to have a picture taken.
It is claimed Mbappe said: "I cannot take a photo with that shirt."
This afternoon Mbappe featured for Monaco in their pre-season clash with Stoke.
Speaking earlier today, Arsenal boss Arsene Wenger claimed no bid for Mbappe had been made by the Gunners and said it was unlikely the player would be sold this summer.
Kylian Mbappe featured for Monaco in a pre-season game against Stoke
He said: "It looks like that. Maybe he had too much choice, so in the end people don't move."
He added: "That’s not true as well. People have a big imagination. What we know now about Mbappe is that it’s over £100m.
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"After that it’s free to imagine what you want. But we have not made an offer. It looks like he will stay at Monaco [for one season].
"Too much choice maybe, so in the end people don’t move!"