The Manchester Evening News says United have agreed terms of around £5m with Colombia's Fortaleza EIF for the 17 year-old midfielder.
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No contracts have been signed, though there is a verbal agreement between the two clubs.
Orozco will move to United this summer as he turns 18 on July 13, so clearing him to leave Colombia according to FIFA rules.
The youngster is viewed as one for the future and will initially be registered with the U21 team at United.