Manchester United and Real Madrid have been linked with the 18-year-old forward in recent weeks but the club chief has officially reported that Los Blancos have not made any approach for the youngster.
"Yes, he has a clause and it's quite big".
Mbappe will play in a Champions League semi-final after he helped Monaco defeat Borussia Dortmund, scoring three times in their 6-3 aggregate win over the German side.
City's interest in Mbappé is no secret and they tried to sign him last summer before he truly broke out, but Monaco rejected a £34.5 million bid for a player who at the time was a relative unknown with few senior games under his belt.
"Yes, he has one - but it's a lot, a lot of money", he said. "I don't have his contract so I don't know exactly how much, but it's a lot", Cordon confirmed to Cadena Cope.
France worldwide Mbappe has enjoyed a breakout season, scoring 22 goals - including five in four Champions League knockout games - and has reportedly attracted interest from a number of top sides.
In turn, that has naturally led to speculation linking him with the biggest clubs in Europe, although his more immediate focus will be on helping Monaco finish the job and complete what would be a stunning double.
Prince Albert of Monaco, who remains involved behind the scenes at the club, told RMC he hoped Mbappe would stay for another season.
Los Merengues have been cited as just one among many teams thought to be seeking Mbappe's signature following his break into the elite ranks of world football this season.
"Juventus are a very hard opponent, but all of the teams left in the semi-finals are massive teams", he said.
'In the locker room Mbappe was very sad, nearly cried, he was really down.