The Colombian forward is widely regarded as one of the very best players on the planet, and only completed a £50m move to the newly promoted Ligue 1 side over the summer.
However, Falcao is already thought to be considering his options after failing to settle in the Principality.
The 27-year-old was lured to the Mediterranean coast with the promise of a €14m-per-year contract, but is instead earning around half of that figure.
Allied to this, he is also concerned by the lack of atmosphere at Monaco’s Stade Louis II and is unsure as to whether he can build on his burgeoning reputation at the club.
Jose Mourinho wanted the South America sensation over the summer, but missed out on a deal and is said to be frustrated by his current attacking options.
As a result, he is ready to launch a loan raid for Falcao, in the hope that the player’s desire to move on may be enough to push through an agreement.
Manchester United are also keen, but it is believed that the ex-Atletico Madrid man’s favoured destination would be Stamford Bridge.