The club's assistant coach Jean Petit has confirmed negotiations for the Colombian are progressing and that he hopes to see a number of other top players follow
The Atletico Madrid star has long been linked with a shock move to the newly-promoted Ligue 1 outfit, despite reported interest from the likes of Real Madrid, Chelsea and Manchester City.
Petit has now confirmed he expects the Colombian to seal a move to the principality club shortly, along with a number of other top-class players.
"Yes, we are expecting Falcao and four or five other players of his quality," he told Radio RCN.
"We have spoken and we continue to speak with Falcao and his representatives, negotiations are ongoing. We hope to seal a deal as soon as possible.
"Monaco need a player like Falcao because he can help us a lot and because he can attract other top players, and that's the best way of confirming our project is big and interesting. Signing Falcao is a big coup, on sporting and media levels, for French football.
"As a footballer Falcao has everything. He has technique, good control of the ball and scores a lot of goals. We saw it here in Monaco in the [European] SuperCup final and we were impressed and surprised by his performance and clinical finishing. President [Dmitry] Rybolovlev likes Falcao a lot."