Chelsea, Manchester City and Real Madrid have been heading the chase for the brilliant Colombian - who is being tipped to leave the Vicente Calderon this summer.
Falcao has insisted he is more than happy at Atletico, who have already secured Champions League football for next season.
But Monaco - who are set to seal promotion back to Ligue 1 - are ready to spend big with Russian owner Dimitri Rybolovlev set to back a deal which would cost €60million.
But Cerezo did his best to laugh off the speculation suggesting Falcao could be heading for the Principality.
"Now Falcao's going to Monaco? We are going to go around the whole world!" said Cerezo.
"Falcao is a specialist at playing in finals and, in the end, he can help us win them."
Cerezo says that Atletico and Falcao are focused on the Copa del Rey final next week, which sees them clash with rivals Real Madrid.
"Finals are there to be won but nothing is easy and we intend to go out there with all the enthusiasm in the world to achieve success, " he said.
Monaco coach Claudio Ranieri would not be drawn on Falcao, and attempted to play it down, saying: "Falcao will join Monaco? Oh yes, just like Beckham. I like rumours too. When he will come I will tell you."