Depay, 26, has been linked with the Catalan club following the appointment of Ronald Koeman as head coach.
Koeman was in charge of the Netherlands previously and had a very good relationship with Depay.
If the latest reports are to be believed, Depay will soon be working with Koeman again at Camp Nou.
La Vanguardia claims Barcelona are on the verge of signing Depay for €25m by the ‘express request’ of Koeman.
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The former Manchester United player only has a year left on his Lyon contract, which would explain the low transfer fee.
Depay has been a sensation since heading to France with 57 goals and 43 assists in 139 appearances.