The Colombian ace is expected to miss the rest of the season with a knee problem, which is also threatening his participation in the World Cup.
Chelsea were heavily linked with Falcao last year, but were unable to compete with the financial muscle of the Principality-based side who snapped him up from Atletico Madrid in a big money deal.
However, the South American hit-man is already said to be considering his future at the Stade Louis II, which has opened the door for a shock exit.
Jose Mourinho is known to be in the market for a top class centre-forward, and sees Falcao as an ideal option.
Despite his fitness concerns, Monaco are far from keen to sell and may ask for around £60m to consider letting him leave the Mediterranean coast.
Arsenal have also been linked with the forward, but with Mourinho’s agent Jorge Mendes also the player’s representative a deal could be smoother for the West Londoners.
PSG’s Edinson Cavani and Diego Costa of Atletico are also on Chelsea’s radar.