He reports on his website: "Suso has reached an agreement with AC Milan on 4-year deal with annual salary of around €1.5 million net.
"It still needs to be determined if Liverpool will let him leave for Italy in January in exchange for a small financial package or if he'll join the Rossoneri on a free transfer in June."
The 20-year-old's contract expires next summer, and he is yet to agree on a new one, despite stating in March he was open to signing an extension, reported by the Liverpool Echo at the time.
Suso is yet to feature for Liverpool this season, but only just last week he told Liverpool's website how much he enjoys Brendan Rodgers' training sessions.
Last season he was on loan at La Liga side Almeria, where he impressed scoring three goals and providing seven assists.