The Red Devils have made the Spain international their number one target as they seek to strengthen their striking department ahead of the 2017/18 season.
United have been in lengthy talks with Real over a deal, with manager Jose Mourinho keen to land Morata, 24, for the beginning of the club's pre-season tour of the United States next week.
Goal also understands that Morata, who is currently on holiday, does not want to return to Real's pre-season camp with his heart set on joining United, with all but the fee agreed between the three parties.
However, although United have increased their offer from €70m (£61.5m) to €80m (£70.2m), Real have rejected the bid as they look to make a significant profit on Morata.
Man Utd target Morata takes a boat trip
Alvaro Morata's on his boat again! Manchester United fans be like... that better be stopping in Manchester! Posted by Goal.com on Wednesday, 5 July 2017