The Colombia international is currently on loan at Old Trafford from AS Monaco, but he has failed to live up to his considerable reputation, scoring just four goals in 29 appearances to date.
He has one last chance to add to that tally – should he feature against Hull City this weekend – but the report claims United manager Louis van Gaal has already informed the striker of his decision.
Falcao was reportedly told that he would be leaving United this summer at some point in the last 48 hours, and the 29-year-old has now allegedly informed his agents to start working on a new destination for him in the Premier League.
The report claims the striker would favour a move to London, but it remains to be seen if the likes of Arsenal, Chelsea or Tottenham Hotspur would sign a striker who has so far failed to prove he can score regularly in the English top flight.
That said, with a full pre-season behind him he could yet prove the doubters wrong.
The report goes on to claim that both Rafael and Jonny Evans will also be told they are available for sale this summer, along with Nani and Anders Lindegaard.