Former Reds boss Rafa Benitez shelled out £17million for the Italian playmaker last summer as a replacement for Xabi Alonso, who moved to Real Madrid.
Aquilani, however, failed to recover from a serious injury all season, with Benitez lacking faith in the player's fitness and often leaving him on the bench.
The appointment of Hodgson, however, has seen a new opportunity for the 26-year-old to make an impression and show his fitness, and the new Reds boss admits he has been impressed with what he has seen so far.
"We have done a lot of tactical work with our fitness people but we've only really scratched the surface," said Hodgson.
"Alberto has come out of it very well, as has Lucas, who is the only player who can really say he is a Liverpool first-team regular.
"But Alberto has got to use this pre-season to put all his fitness problems behind him. What I have seen in the last three weeks working with him has been encouraging and he's working well."