The Colombia striker has long been linked with a move away from Atletico Madrid with Manchester United and Chelsea mooted as possible destinations.
However, it appears that Monaco have jumped to the head of the queue with the newly-promoted team having already recruited highly-rated Porto pair Joao Moutinho and James Rodriguez for a combined fee of around £60million.
President Dmitry Rybolovlev is highly ambitious, evidenced by his capture of the Porto pair, who are former team-mates of Falcao who has scored 32 goals in 36 appearances this season.
Atletico manager Diego Simeone has already said he will not bear any grudge if the 27-year-old leaves, and Sunday night's Primera Division match against Real Mallorca at the Vicente Calderon is looking increasingly likely to be his last home game for the Rojiblancos.
Monaco assistant coach Jean Petit is reported to have told Radio RCN on Friday: "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 out project is big and interesting.
"Signing Falcao is a big coup on sporting and media levels for French football."