The English midfielder has been on a successful season-long loan at French side Lille, where he played alongside Chelsea's new signing Eden Hazard while Aquilani also spent last term at Italian giants AC Milan, where he made 23 appearances in Serie A.
"The boy Aquilani is a wonderful talent and a terrific player but he might not be able to settle" - Brendan Rodgers
"They're certainly talented players," Rodgers told the club's official website.
"I know Joe [Cole] well from my time at Chelsea. He's a wonderful talent.
"I thought [Alberto] Aquilani was a really good player. I'd seen him in the Champions League and he came to Liverpool but it didn't quite work out and he went back [to Italy] on loan.
"There might be other situations. I just need to find out from speaking with those players because there are always other reasons.
"The boy Aquilani is a wonderful talent and a terrific player but he might not be able to settle. He might not be able to adapt to the country so you've got all those issues and sometimes you're not aware of that until you sit down and speak to the people."