The Gunners are reported to be scouting the 14-year-old youngster but could also face competition from Juventus and Borussia Dortmund.
United are however, favourites to clinch a deal after bringing the youngster to their training grounds in Carrington and holding talks with his father and representative Habib Antar who brokered the Sofiane Fehgouli deal to West Ham.
The 14-year-old is one of the brightest talents in Turkish football and has already broke into the youth Turkish national team setup.
Cogalan does have another five-years left on his current deal with Valencia but his father Sedat did reveal that they will consider United’s offer.
Ferhat’s father Sedat 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?”
Cogalan moved to Spain aged 12 and has played in Valencia’s youth setup ever since scoring 22 times and provided 30 assists for the La Liga outfit last season.