The Italian international underwent ankle surgery in May and is only expected to be fit in the next "four to eight weeks".
Aqulilani agreed a five-year contract with Liverpool after Reds boss Rafael Benitez identified him as his preferred replacement for Xabi Alonso, who joined Real Madrid for around £30m earlier this week.
Liverpool had a bid of around £20m for the 25-year-old accepted by his Italian employers on Wednesday before the player headed to Merseyside for a medical and contract talks.
The now former Roma man is expected to be at Anfield on Saturday to witness his new team-mates take on Atletico Madrid in the club's final pre-season friendly before next weekend's big kick-off.
The crocked midfielder is believed to be earning around £80,000 a week.