The La Liga club's general manager Miguel Angel Gil Marin says that the striker "has earned the right" to consider his options at the end of the current campaign
The striker has long been linked with a move away from Vicente Calderon following his scintillating form in 2012, with Chelsea and Manchester City believed to be at the front of the queue for his signature.
Falcao, however, has stressed that he has no plans to depart the club in the January transfer window, and Marin says that discussions will be left until the end of the season.
"He's a great player," Marin told AS. "He is one of the best in the world and has now been awarded as such in Dubai [at the International Sports Conference].
"By signing him when we did, it was very high risk. Thank God that it went well. People doubted him and the amount that we had paid. Our trust in him has been proven. We spoke with him before he came and we were right about the player, as a professional and as a person.
"What about his future? The commitment to him is that at the end of the season we will decide what is best for both parties and we will help him to decide, he has earned the right to decide.
"I know that he is comfortable in our league, in our city and at our club."