The 21-year-old forward opted to leave Anfield in January, having failed to break into the first team under Brendan Rodgers and spending time on loan at Almeria last season.
However, he has only experienced 10 minutes of action at Milan to date, in a Coppa Italia defeat to Lazio in January.
Suso admits settling into life in Italy has taken time, but hopes to earn a starting role in the near future and help Milan climb the Serie A table.
"I am continuing my adaptation to Italian football, I continue to work to blend in," he told the club's official website.
"I would have liked to have taken the field a bit more, but I am waiting for my chance. I would love to become an important player for this team.
"My greatest aspiration is to have success with Milan, my goal is to always give my best.
"The position where I play best is as a playmaker, last year I played as right wing, left wing, and in the past as a midfielder, but I will play wherever the coach wants [me to]."
'Mourinho called and said, "You want to play for me?" I said, "Yes sir". He replied, ‘I'll see you in Milan tomorrow" then put the phone down - I signed for Inter the next day': How Jose Mourinho easily persuaded Premier League star to make Serie A move
‘If I score only one time, I’ll go to Southampton. If I score two times, I’ll go to Leeds. If I score three times, I’ll stay’ Liverpool’s Cody Gakpo on learning the game and almost joining Leeds United
