The 28-year-old has arrived at Carrington for a medical and to finalize terms of his loan deal from Monaco.
The 28-year-old will undergo a medical and finalize the terms of his switch before the transfer window closes.
Goal understands that United will pay a 10 million pound-plus fee for the Colombia international, as well as a significant part of his £300,000-a-week salary.
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United is also expected to complete a deal for Ajax defender Daley Blind before the deadline which will take United’s total spending this summer to a figure close to £160 million.
Manchester City appeared to be closing in on the signing of Falcao after the striker’s proposed move to Real Madrid fell through at the end of last week.
The Colombian, who required surgery to repair a damaged anterior cruciate ligament in January, was targeted by City as a replacement for Alvaro Negredo, who has agreed to join Valencia on loan.
Arsneal manager Arsene Wenger had also sanctioned a pursuit of Falcao with the same agreement as United has reached with Monaco.