The Blues may have to cough up a significant figure to secure the player, but it represents a huge drop in the fee he moved for just last summer.
Colombian striker Falcao has one of the most impressive goal ratios in European football.
A five-year spell in Europe has seen the forward plunder goals in Portugal, Spain and France, and he is quite rightly held up as one of the best centre forwards around.
And it looks like he may be able to add accelerated healing powers to his list of abilities, looking odds on to recover from a cruciate ligament injury he sustained in January to lead the line for his nation in this summer's World Cup.
After a difficult first season in France with Monaco, where he had to carry the hopes his club had of overtaking PSG, hopes that were eventually hit by his season-ending injury, French sports newspaper L'Equipe have reported that the principality club would be willing to cash in on the 28-year-old for €45 million, roughly £36 million.
This may prick the ears of Mourinho, who is famously in the market for a forward and is about to suffer a cash windfall from the sale of David Luiz to PSG.
That Monaco are willing to take a hit on the €60 million they shelled out to bring Falcao to the club is likely down to his injury, and the fact he will turn 29 over the course of next season.