The 18-year-old has positioned himself in the shop window with his exploits during a breakthrough campaign in 2016-17 which delivered 26 goals, the Ligue 1 title and senior worldwide recognition.
Madrid are believed to be the club closest to sealing his signature, where he would work under compatriot Zinedine Zidane, though he was more coy when asked specifically about those links.
'We're going to go away with the family and we'll think about what's going to happen, ' said Mbappe after France's 3-2 win over England. "I'm under contract, I'm not free".
The striker also addressed the Spanish capital club's interest in taking him to the Santiago Bernabeu this summer.
Gab Marcotti and Steve Nicol see no reason why Gareth Bale couldn't stay at Real Madrid if they were to sign Kylian Mbappe.
"[The Champions League] is a dream, a competition that everyone wants to win and that only a minority can win - the most important are the titles", Mbappe said this week.
"I don't know what is going to happen with him but he played a fine game against England and he is a very good player".