It's unclear whether it will be at the end of the season, or during this transfer window.
Suso is out of contract at the end of the season and rumours have persisted about the future of the Spaniard but his time is coming to an end.
His agent Jaime Serra said: “Yes, I can confirm that there is an agreement between Milan and Suso on a four-year contract.
“There’s a possibility (he will arrive in January). We’ll just have to see what happens between now and the end of the transfer window."
The 21-year-old, who will leave on a free transfer, is highly regarded amongst a lot of Liverpool supporters and they will be disappointed to see him leave.
He featured fairly prominently in Brendan Rodgers' first season in charge at the club in both the Premier League and Europa League before joining Almeria on loan last season, helping the La Liga side survive in the top flight in Spain.
He returned to the club in the summer and had a promising pre-season but his first team chances have been blighted by injury, having only recently returned to full training following groin surgery.
Suso made one notable contribution this season when he scored both in extra time and in the penalty shoot-out of the League Cup third round win over Middlesbrough in September.
The Liverpool Echo reported that discussions took place over the summer with regards to a new deal but no agreement could be reached.