The Colombia international eventually left Monaco for United on deadline day of the summer transfer window, but Falcao's father Radamel Garcia has claimed that Louis van Gaal's side faced stiff competition from a number of European top teams.
"Juventus, Manchester City and Liverpool all wanted him as well, and even Arsenal made a late approach," he told LA FM. "Fortunately, he has now joined Manchester United. They are a great team."
The 28-year-old was also heavily linked with a move to Real Madrid, but the Santiago Bernabeu side eventually opted against signing the prolific striker.
"Real Madrid? When you have money and go to the market to buy a shirt or pants, you have to decide whether you buy them now or not. Real Madrid eventually opted not to do so and there's not much you can do about that.
"Plus I got the feeling that there were quite a few conditions if they wanted to sign him. We have to accept how things went.
"We are very grateful that Manchester United came along. United are England's most important team and one of the strongest economic powers in football."