Falcao's impressive performances this season for the Colcochones has led to many clubs reportedly showing interest in his services, including Los Blancos.
However, Cerezo has made it clear that there is no substance to the suggestions made on Punto Pelota that his star player is set for a switch to the Santiago Bernabeu.
"I want to say that it is false that Falcao has an agreement with another team. I say it is false because I have [not] spoken to anyone regarding this subject," Cerezo told Marca.
"It is absolutely false and a lie. It is one thing to joke but it is another to make a something out of nothing. Above everything, I don't like having words put in my mouth that I have never said.
"Like [club general manager] Miguel Angel Gil said, Falcao is our player and he has won the right to make his own decision. He has a contract with us and there is no need to talk nor invent anything else."
"The renewal of his contract will be done with tranquility and will occur over the course of the year," he continued.
"There is no date nor day nor place by which it needs to happen. There is no problem and it will happen when it can. We do not know if he has offers from other clubs though I do imagine he will have since he is a very good coach."