The Colombian marksman is one of the most prolific strikers in the world and he is being constantly linked with a move away from the Vicente Calderon.
Chelsea have long been linked, but he has also been tipped to move to Atletico's city rivals Real.
Reports in Spain had suggested that Falcao, along with his agent Jorge Mendes, had dinner with Perez and discussed his future.
But Falcao had angrily denied this, saying: "Everything is a lie."
"Lately there has been all kinds of reports about me," the 26-year-old said on Antena 3 this week.
"All those that say I ate with Florentino are false. Neither is it true that I travelled with Cristiano Ronaldo to the Ballon d'Or gala."