The 14-year-old is one of the brightest talents in Valencia’s academy and is said to be interesting a host of top clubs.
According to Valencia based website Super Deporte, the teenager, his father Sedat and agent Habib Antar met with representatives from United last week.
The report says Cogalan has a training contract until July 2021 but he can still be signed by another club.
United are understood to be at the front of a queue which includes Arsenal, Juventus, Bayern Munich and Borussia Dortmund.
Cogalan’s father told French website La Voix Du Nord that United’s proposal has piqued their interest.
He said: “We’re in no hurry because Ferhat is in contract with Valencia until 2021.
“But when a club like Manchester United invites us, it is logical that we study the proposal, right?”