The report also claims the 29-year-old wishes to find another club in England, with London his preferred destination, so which of the four London clubs below is he most likely to move to?
Here we consider whether the current United loanee could be turning out for Tottenham Hotspur, Arsenal, Chelsea or West Ham United next season.
Of all the top London clubs currently in the Premier League, Tottenham does at first glance seem the most likely option for Falcao if he remained in England.
After all, Mauricio Pochettino’s side need new strikers and with Emmanuel Adebayor and Roberto Soldado both flattering to deceive this season, Falcao could in theory walk straight in as second-choice front-man behind Harry Kane.
That said, while Tottenham may be tempted, his wages would be sky-high and there would be a considerable outlay even if they did sign him on loan.
Arsenal could certainly afford Falcao’s wages and any potential transfer fee but of all the clubs on this list they are the least likely to move for him.
With Danny Welbeck, Olivier Giroud and Alexis Sanchez on their books and the likes of Chuba Akpom breaking through, why would the Gunners move for the 29-year-old?
With Didier Drogba leaving Chelsea this summer, a Falcao move to Stamford Bridge would not be beyond the realms of possibility.
Jose Mourinho certainly knows the player well and as a back-up to Loic Remy and Diego Costa he would be a fine addition.
But would he move to a side where his chances of regular game-time would be as limited as they proved at United?
The outside shot it may be, but a move to West Ham could be exactly what Falcao needs.
West Ham have struggled for goals in recent times despite the presence of the likes of Enner Valencia and Diafra Sakho, and with Andy Carroll still suffering from injuries the Colombian could be another unexpected star-name to arrive at Upton Park like Carlos Tevez before him.
Again though, it would take a lot of money to pay those wages.