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Ultras Monaco 1994 took to Twitter to claim that the reported Paris Saint-Germain and Real Madrid target had "proved nothing special in his few dozen matches as a professional".
Mbappe was left out of Monaco's squad for Friday's Ligue 1 outing at Metz as speculation intensified surrounding the teen sensation's future.
"Kylian is not at 100 percent. He is not in great form. But that is to be expected of a kid who is just 18," Monaco coach Leonardo Jardim explained.
Mbappe's new employers will have to meet a reported 180 million euros ($211 million) price tag to secure the services of a player who scored 26 goals in 44 matches last season.
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The club's Ultras said they were "amazed and indignant" at the amount of money "involved in Mbappe's transfer and in his salary to extend his contract".
"No player is worth so many millions of euros," argued UM1994.
In their Twitter criticism Monaco's Ultras spoke of "the love and respect for the shirt of the club that helped shape him for life".
And they reminded Kylian Mbappe "and his entourage" that "nothing or no one is bigger than AS Monaco."
Their statement concluded with a vote of confidence in the club's directors "to construct a team capable of defending our title with or without Mbappe".
Monaco have lost three key members of the title-winning team this summer.
Full-back Benjamin Mendy was sold to Manchester City for a reported £52 million (58 million euros, $67 million) fee, a world record for a defender, last month, joining Portuguese playmaker Bernardo Silva at the club.
Powerful midfielder Tiemoue Bakayoko meanwhile joined Chelsea.