The Blues have been monitoring the Colombian for some time, and were linked with a move for his signature prior to his £50m transfer to the French club over the summer.
Rumours suggest that Falcao has struggled to settle on the Mediterranean coast, with concerns surrounding his ability to develop as a player at the forefront of his mind.
This, coupled with continuing concerns regarding Financial Fair Play at the club, has led to talk that he could be allowed to leave in a mega money deal this January.
Chelsea are interested, and have even contacted the Principality-based outfit to discuss a potential deal.
It is thought that Monaco value their star man at around £80m, which is a significantly higher fee than they fee they paid Atletico Madrid a matter months ago.
The London club could explore a possible swap deal, in which Fernando Torres and Demba Ba could be sent to the club to replace a chunk of the cash pay-out.
Jose Mourinho is thought to have made a centre-forward his major target for the coming windows, with a lack of goals from his current crop of strikers a major concern.