Aquilani is currently on loan at the San Siro and just three appearances shy from triggering a clause in his loan contract which would allow the Rossoneri to snap him up.
The 27-year-old agreed the one-year loan deal with the Serie A champions last summer after failing to make it into Liverpool manager Kenny Dalglish's plans.
"Putting on Milan's shirt forces you to win," Aquilani told Milan Channel.
"Milan are at the top in Italy and Europe and you realise that right after you enter Milanello [training ground] .
"I hope I can stay at the club after this season, but I am not sure that this will happen.
"I saw that there was an opportunity to join Milan last summer and in the end my hopes were rewarded."
Aquilani has so far made 22 competitive appearances for the Rossoneri.
The Italian joined Liverpool from Roma in 2009 but spent last season on loan at Juventus. He is under contract with Liverpool until June 2014.