The Colombia international took the decision to head for Ligue 1 over the summer in a £51million deal, with Monaco's ambitious project appealing to him.
It was, however, suggested when he made a move that Monaco were being viewed as a stepping stone back to Spain.
With former employers Atletico Madrid reluctant to do business with cross-city rivals Real, Falcao was forced to look elsewhere when interest in his services mounted.
Real are refusing to concede defeat in their pursuit, though, with president Florentino Perez claiming: "Falcao is a great player and I am aware he wants to play for Madrid."
The prolific 27-year-old is reluctant to be drawn into another debate regarding his future, though, with his contract in Monaco due to run until 2018.
Falcao, who has netted seven goals in nine appearances this season, told reporters while away on World Cup qualifying duty with his country: "I can only thank Florentino Perez for what he's said, but I must respect my current club Monaco, where I am feeling very well.
"I am very happy at Monaco. This is not the time to talk about Real Madrid's potential interest in me out of respect for my current club."
While speculation is set to rumble on, Falcao's team-mates at Monaco are convinced he is settled in France and not looking for a move elsewhere.
French midfielder Jeremy Toulalan told L'Equipe: "In football you can never say never, you never know what is going to happen, but Falcao has been outstanding for Monaco so far.
"With what he has shown so far, unlike some forwards, you can see he is working hard for the collective cause. I don't think he wants to leave."