The young Spaniard was linked with a deadline day loan switch to the San Siro, but the arrangement failed to come to fruition.
But that has not deterred the Rossoneri, who are now eyeing a 2015 deal for the playmaker.
Suso is now in the last year of his contract, and reports claim that he’s reached a verbal agreement to link up with them when the season ends.
Due to his age, 20, Milan will be obliged to pay Liverpool a compensation sum – which could be around £2m-£3m – but they are willing to do so for the talented starlet.
Suso burst onto the scene at the same time as Raheem Sterling as Brendan Rodgers put his faith in young players during the opening months of his tenure at Anfield.
But unlike the now England star, the silky passer was loaned out last season to gain experience, which he got with Almeria in his homeland.
Although he claimed recently to be happy on Merseyside, Di Marzio says that the player is keen on a move to Milan, with his route into the Reds’ XI is blocked by a host of more experienced players.