The 21-year-old Spaniard is out of contract in the summer and has struggled to make his way into manager Brendan Rodgers’ plans at Anfield.
It is being reported he has agreed a four-year deal to play at the San Siro.
He has not featured for the Liverpool first team since their Capital One Cup penalty shoot-out win over Middlesbrough on September 23.
Suso has also struggled with a groin injury in the last few weeks but produced a lively display earlier in the week for Liverpool’s U-21 side in their 2-0 win over Shrewsbury.
Suso, who joined the Reds in July 2010 from Cadiz and was on loan at Almeria last year, has made 21 appearances for Liverpool.