The 27-year-old's proposed loan move to Fiorentina earlier this summer reportedly broke down after the Italian admitted that he is only interested in a permanent deal.
However, while the midfielder recently told reporters that he is happy to remain at the Merseyside club, he didn't rule out the possibility of returning to Italy.
"[AC Milan CEO] Adriano Galliani knows all the facts and he is well informed and we heard what he said last week," Aquilani's agent Franco Zavaglia told Itasportpress.
"Milan said they need a left-sided midfielder and so we cannot exclude this possibility."
The Italian signed for the Anfield club in 2009, but has struggled with injuries and has made just 18 appearances for the club.