The 27-year-old Colombian, who has been linked with big-money moves to Europe’s top clubs, has scored a remarkable 70 goals in 90 matches over two seasons at the capital club.
But the club's CEO Miguel Angel Gil Marin said that the player would be allowed to pick his destination due to an agreement between both parties.
“Before the start of the season we talked with Falcao and promised him that if he kept the same performance and helped us into the Champions League, we would help him,” Marin admitted.
“Whatever decision he takes, we will be with him. We know what makes a good striker – we have sold and replaced Fernando Torres, Diego Forlan and Sergio Aguero.
“And now it is Falcao. I don't exactly who will be here next season, but you can be sure that Atletico will have a strong team.”
Despite leading Los Rojiblancos to Champions League qualification and the Copa del Rey title this campaign, Falcao has been widely expected to leave Atletico.
La Liga's third-top scorer has been linked with Chelsea, Manchester City and Manchester United, but has also been tipped to join one of the cash-rich French sides Paris Saint-Germain and Monaco.