Suso, 25, had joined Liverpool in 2010 when he was 17.
But he failed to make much of an impact at Anfield and joined the Milan giants in 2015 when his contract expired.
The midfielder has netted 23 goals and made 35 assists in 135 appearances for the Serie A club.
Milan have one final Serie A match of the season left – a crucial clash against SPA – as they hope to brighten their chances of qualifying for the Champions League with a win.
But they will also need their city rivals Inter Milan to slip up against Empoli.