The club's president says he wants to stay at the Vicente Calderon for another 25 years with the Colombian striker leading the line throughout
The Colombian was pivotal to his side's Europa League and Super Cup successes but Goal.com has since confirmed the interest of Chelsea and Manchester City, while the player's father claimed his son was keen on a move to Real Madrid.
However, Cerezo is keen to hold on to the former Porto striker as they look to break the Liga monopoly of Barcelona and los Blancos.
"I hope to be here another 25 years with Falcao. With his father, I do not know, but with him I hope so," he told AS.
"I am excited and very happy about this, because to be a leader of a football club for 25 years is very difficult. I have the desire and enthusiasm to continue longer.
"There have been ups and downs, but I'll stick with the first, with the times that we had fun. There have been many and in twenty years we have won eight titles.
"Football is a matter of stages and hopefully both teams will weaken, they have to. I, for my part, want to continue in football."
Cerezo's predecessor Jesus Gil died in May 2004, having led the club through one of its most successful eras, and the 64-year-old was quick to pay tribute to the former president.
"I can say many things about him, but above all, I will say that he was a great friend."