The Italy international is reported to be a target for Liverpool, while Arsenal have expressed an interest in the creative midfielder in the past.
A move to Anfield has been touted in the wake of Real Madrid's continued interest in Xabi Alonso, with Aquiliani seen as an ideal replacement should the Spaniard head home.
Roma have previously maintained that they would be unwilling to part with the talented 25-year-old, but boss Luciano Spalletti has revealed that stance could be about to change.
"We need to be open and listen to any type of offers that are proposed to us," he said.
"We are not worried, we know what we need to do.
"There will probably be two or three transfer market deals done and I am convinced we will be able to work well."
Aquilani is under contract with Roma until 2013 and despite Spalletti's admission, club director Bruno Conti insists no approach has been received as yet.
"The situation as it is right now is that Aquilani will remain until there is a team that makes an offer," Conti said to Mediaset.
"Once this happens then we will see."