Dalot has a release clause of €20m (£17.5m) but it is understood this is yet to be triggered by United for a player who made his debut last season, finishing with seven appearances, six of which were in Porto's triumphant domestic campaign.
Porto had hoped to hang on to Dalot for at least another season and had rebuffed interest from other clubs. Porto are understood to have turned down bids below Dalot's release clause previous year.
He was included in the UEFA European Under-17 Championship and the UEFA European Under-19 Championship teams of the tournament and he won the Primeira Liga title in his first season with the club.
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Emily Nipps, A spokeswoman for the airport, said: "I've never seen anything like this in an airport, or otherwise". The owners told reporters they planned to get some rest before driving the new pup family to Pennsylvania.
Dalot has been described as a modern full-back who is comfortable in attack, with good delivery and an eye for goal, and has operated in midfield.
Mourinho lacks faith in United's right-back options beyond Valencia, who is 32 and needs back-up for his position to allow him to be rotated.
Manchester United, however, will continue their spending spree with Shakhtar Donetsk's Fred widely expected to be the next player through the door at Old Trafford.
United are exptected to offload Matteo Darmian to Juventus for £11.5 million in order to make room for the incoming Dalot, with the Italian failing to impress United boss Jose Mourinho during his spell at Manchester.