Falcao has attracted interest from several of Europe's richest clubs and his five-goal haul in Atletico's 6-0 La Liga win at home to Deportivo La Coruna on Sunday will only have served to boost his market value.
Construction magnate Perez was sitting at the same table as Falcao and Real captain Iker Casillas at an awards ceremony in Madrid and was caught on camera saying to Casillas: "I'm going to ask for a serviette and give it to Falcao".
Perez was referring to an incident at a gala in Monaco in 2000 when he made an offer to Zinedine Zidane by writing "Do you want to play for Madrid?" on a serviette and delivering it to the former Real and France midfielder.
"Be careful they are recording this," a laughing Casillas responded, pointing to the television cameras.
Media reports have suggested English Premier League side and European champions Chelsea and Qatar-owned Paris Saint-Germain are among clubs interested in signing the prolific 26-year-old Colombian, who is known as "the tiger".
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.