Aquilani is determined to prove his worth to Rodgers during pre-season after spending the last two years on loan back in Italy at Juventus and AC Milan.
The 28-year-old has made just 18 Premier League appearances since joining the Reds in 2009, but speculation continues to link Aquilani with a return to Serie A.
His omission from Liverpool's friendly against Tottenham Hotspur on Saturday only served to fuel rumours regarding his future and Rodgers is still to decide whether Aquilani will be part of his long-term plans.
"The situation with Alberto is simple," said Rodgers in the Daily Mirror. "I have wanted to assess him over the first few weeks of training.
"Over the course of the next week, I will make a decision on what's going to be best for us, whether he will be useful for the group or whether it's best for him to move on."
Reports have claimed a deal in the region of £7million is close to being agreed with Fiorentina, but Aquilani's representative Franco Zavaglia says there has been no contact with the Viola.
"Let us not open up a soap opera, please," agent Franco Zavaglia told Radio Sportiva.
"Aquilani is a Liverpool player and he is happy where he is now. We have not received any requests from Daniele Prade, but that was only to be expected, seeing as Aquilani will only leave on a permanent move and at figures Fiorentina cannot afford.
"I would rule out a current return to Italy."