Depay has shone for Holland alongside Reds pair Virgil van Dijk and Gini Wijnaldum.
Speaking to Bwin, Pires said: “Depay wants to come back to the Premier League and he feels he has unfinished business in England.
“He perhaps feels he wasn't given a chance to perform and earn the right to stay longer considering he was so young and showed glimpses of undoubted potential. Depay might want to return to Manchester United or he might be motivated to prove them wrong by performing for one of their rivals in the Premier League."
Depay, who is rated at around £45m, signed for United in 2015 for a reported £25m in 2015 but left less than two years later, having scored only two goals for the Red Devils and started only one game in his second season at Old Trafford.