Falcao has flown in from Nice and is now due to undergo a medical ahead of a loan that is worth between £5-6m to Monaco.
The last 24 hours have seen the Colombia international linked with a host of Premier League clubs including Arsenal and Manchester City as well as European champions Real Madrid.
Real appeared to be favourites to sign Falcao after he tweeted "Hello Madrid" on Saturday – only to delete it not long afterwards, but United now look to have won the race to sign the 28-year-old.
Niall Quinn says Falcao’s move is Louis van Gaal’s way of inspiring a team that has yet to win a Premier League game this season, despite the arrival of Angel di Maria, who made his debut in Saturday’s 0-0 draw at Burnley.
“If Falcao comes then I think it is fantastic competition for places because when you look at how the game is played now, it is no longer an 11-man game – it’s a 14-man game every week,” Quinn told Sky Sports News HQ.
“The way the game is going that’s going to become more dependent on players coming in, making an impact and being flexible and moving around.
“This will actually kick Wayne Rooney and Robin van Persie on a little bit – they’ll be thinking ‘ok, we’ve got to fire even further than we have been’.
“To make Manchester United improve, Louis van Gaal doesn’t just rely on reputations – he builds his teams around people pushing each other and really buying into his philosophy, but also increased competition and Falcao coming to Manchester United is a wonderful lift to the football club if it comes off.”
The arrival of Falcao saw Javier Hernandez leave Old Trafford as Van Gaal makes space in his squad.
Hernandez has moved to Real Madrid, and Danny Welbeck is reported to be wanted by a number of Premier League clubs with Sunderland, Arsenal, Tottenham and Hull City all interested.