The 26-year-old joined Liverpool for 20 million pounds from AS Roma before the start of last season as a replacement for Xabi Alonso but has failed to establish himself at Anfield.
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"At the moment we are considering possibly loaning him to an Italian club," Hodgson said. "I didn't want to use him (against Trabzonspor) just in case the loan goes through, because for Aquilani this year it's very important that he plays regular football, every week, as the number one man on the teamsheet.
"I can't promise him that here so if a loan move to Italy could help him in that respect it might be good for all parties.
"It would certainly be what he needs, it would certainly protect the value of the player and when he does return to Liverpool no doubt we will see the Aquilani that we signed before he came here injured last year."
He missed the first two months of last season because of injury and only made 26 appearances in all competitions, scoring twice.
Liverpool beat Trabzonspor 1-0 in the first leg of their Europa League playoff at Anfield on Thursday.
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