Falcao has been a stunning success at the Vicente Calderon following his move from Porto in the summer of 2011.
The Colombia international scored 24 goals in his first season in Spain - Messi claimed the Pichichi with 50, four ahead of 2011 winner Ronaldo - and has already netted seven in six league games this season.
And having also grabbed a hat-trick in the Rojiblancos' 4-1 defeat of Chelsea in the UEFA Super Cup and scored in both of Colombia's World Cup qualifiers last month, Falcao is in the form of his life.
And that has prompted Cerezo to make his bold claim, telling the AS newspaper: "Falcao is the best striker in the world. That is not just my words, I refer to the evidence.
"Nor would I want to swap Falcao for Messi or Cristiano, Falcao is the best.
"Many teams would want him but he plays for Atletico and we are delighted about that."
Falcao's goals have propelled Atletico up to second in the Primera Division standings, two points behind Barcelona.
Cerezo admitted it had been a pleasing start but stopped short of putting them forward as title contenders.
"We are in a good situation, we have made a start in which the team is playing well," he added.
"But now I am just thinking of the Europa League match against Viktoria Plzen (on Thursday).
"We have two very important commitments this week and the league has just begun.
"What is clear, though, is that we are not an easy opponent for any team."