The Colombian, linked with most of Europe's top clubs this summer, looks set to leave Atletico Madrid for the newly promoted French side.
Monaco's assistant coach Jean Petit reportedly told Radio RCN: "Yes, we are expecting Falcao and four or five other players of his quality. 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."