It is rumored that it will cost the Red Devils £42 million and that a down payment may have already been made, according to Marca.com.
Falcao has been hot property across Europe and all the big teams have been linked with La Liga's goal machine, but it looks as though United are favourites for his signature.
What does this mean for Wayne Rooney though? PSG have been interested in bringing the United striker to Paris and president Nasser Al-Khelaifi has recently expressed his admiration for him (via Express).
Zlatan Ibrahimovic, as reported by The Telegraph, is also keen to have Rooney join him at PSG and thinks it would be the best place for him if he were to leave Old Trafford this summer.
Falcao would certainly be a player that United fans would love to see Sir Alex Ferguson bring in, but with Robin van Persie only one season in and Javier Hernandez an excellent striker to have on the bench, will Rooney's services be required?
Rooney has scored 12 EPL goals from just 18 appearances this season, which is actually a brilliant return, but over the last two seasons he has consistently given the ball away at times and has evidently lost the pace he was once blessed with.
Danny Wellbeck would probably stay as he is still learning his trade under Fergie, and as an established England international, he gives something else to the team with his speed and willingness to track back.
United have enough funds to keep Rooney at Old Trafford and still pay a club transfer record for Falcao thanks to a recent sponsorship deal with AON.
However, five top strikers in one team just doesn't fit, and while Rooney is still relatively young at 27, it would be wise to sell him while they can still get a good price for his services.