With Samuel Eto'o, Demba Ba and Fernando Torres all failing to score a sufficient amount of goals for the Blues, Jose Mourinho will surely be keen to sign a new front man at some point.
Whether there is the quality or value available in the January window is questionable, but should the former Porto and Atletico striker become available in any way, Chelsea would surely be interested.
With Falcao available to play in the Champions League, he could be a highly sought after player, with reports suggesting that he is unhappy with his contract.
Still, for Monaco to have spent around £40 million on the Colombian just a few months a go, the prospect of a loan move seems highly improbable.
Furthermore, to see Monaco, who are in the hunt for the Ligue 1 title race, ship him out so prematurely would be unthinkable.
Perhaps next summer could see the 27-year-old reconsider his future, but in the build-up to the World Cup, Falcao will stay in France.