The Colombian says there are no problems him and coach Claudio Ranieri and maintains he will return to action for the Ligue 1 side as soon as he recovers from his thigh problem
Falcao has continued to be linked with a move to Chelsea or Real Madrid despite repeatedly insisting he is content with life at Monaco, having joined from Atletico Madrid in a £50 million deal last summer.
The Colombia international has not featured for the Ligue 1 side since the win over Nantes on November 24, with the club citing a persistent thigh injury as the reason for his prolonged absence.
Coach Claudio Ranieri was forced to deny reports the 27-year-old was seeking a move away from the principality side, and the striker himself has now made it clear he has no desire to force an exit in January.
"I am very happy here at Monaco. I don't have a problem with the coach, just with my thigh," he told reporters at a supporter event.
"I feel better. I will play again soon.
"There is a lot of speculation around me, but I have a five-year contract and I'm very happy here."
Falcao, who has nine goals in 14 Ligue 1 appearances for Monaco this season, has already been ruled out of Saturday's clash with Guingamp due to injury.