The 23-year old England striker, who was signed from Newcastle United by previous boss Kenny Dalglish, had been struggling to find form in the past 18 months and faces serious challenges with Rodgers' style of play.
Reports from Milan suggests that Carroll is being linked with AC Milan, but only on loan move, after Pier Silvio (AC Milan owner Silvio Berlusconi's son), was impressed by the strikers contribution to England's campaign at the Euro 2012 tournament.
"Milan still has its superstars but I'd like to have Carroll at Milan. I was impressed with his strength and his headed goal against Sweden," Pier Silvio was quoted as saying in ESPNsoccernet.
However, Rodgers is yet to take a decision on Carroll's future but he is prepared to him the necessary chances.
"Andy is a player I want to assess and speak with,' said Rodgers.
"Andy Carroll is away on his holidays but we have already had a good chat. There have been many inquiries about our players so I will assess them and hopefully put together a group to help us challenge.
"He's a very, very good player. He's shown that in his short career already. He did fantastic with Newcastle, he's done well at times with England," Rodgers added.
"Is it going to be beneficial for the club? That's the most important thing. Sometimes a player going out on loan - in general, not just Andy - can benefit the club in the long term.
"He's made a massive move to a world-renowned football club and there was always going to be a time of adaptation. You sometimes forget how young these people are. They're not machines," the 39-year old former Swansea boss said.
Meanwhile, Liverpool FC have not recieved any official inquiry from AC Milan but the Anfield bosses have had lenghty discussions with Roma regarding Borini over a deal worth £10million.
Borini was co-owned by Roma and Parma last season, but Roma took full ownership of his contract last month by paying £3.95m.
Meanwhile, Liverpool confirmed yesterday that Luis Suarez and Sebastian Coates will represent Uruguay at the London Olympics.
Liverpool are also closing in to sign Fulham midfielder Clint Dempsey before setting off to a tour of North America in the coming weeks, while Real Madrid have been linked to defender Daniel Agger.