The club's assistant coach Jean Petit has confirmed negotiations for the Colombian are progressing well, and he hopes to see a number of other top players arrive
Chelsea had been confident of securing a deal for the 27-year-old after incoming manager Jose Mourinho highlighted the Colombia international as his priority transfer target this summer, but Monaco, who will play in Ligue 1 next term, have already triggered the striker's £50.7 million (€60m) release clause.
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"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 out 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."