The reliable Mike Verweij and Valentijn Driessen report that Barcelona have struck a deal for the Dutch attacker.
The Catalan club will pay €25m plus €5m at the end of the season, then a further €2m in bonuses.
Barca are already planning an official presentation for Depay and hope to confirm his signing this week.
It will mean a reunion for Depay with Ronald Koeman, who left his post as Netherlands coach to take over at Camp Nou.
In 140 appearances, Memphis has scored 57 goals and delivered 47 assists.