Chelsea have recently been linked with a loan move for the 27-year-old, who only joined the Monegasque club in the summer.
The former Atletico Madrid star is currently sidelined with a thigh injury, although his absence has added fuel to transfer speculation.
However, he insists that he is happy in the principality and hopes to return to first-team action soon.
"There is a lot of speculation around me, but I have a five-year contract and I'm very happy here," he told reporters.
"I don't have a problem with the coach (Claudio Ranieri), just with my thigh. I feel better. I will play again soon."
Falcao has scored eight goals in 12 league appearances this season.