Brendan Rodgers doesn't see the 23-year-old, who Liverpool signed for £35m only 18 months ago, as part of his plans for the upcoming Premier League season.
Newcastle made an unsuccessful offer of a season-long loan deal with a view to a permanent move while paying half the player's wages but the Anfield club rejected the approach and insist they want to do a deal on a permanent basis.
Former Tyneside favourite and all-time Premier League top goalscorer Alan Shearer believes Carroll can get his career back on track at the Sports Direct Arena.
Shearer told The Sun: "Andy is an England centre-forward and I wouldn't say he has been a flop at Liverpool by any means.
"Yes, it took him a bit of time to settle there but he finished the season strongly and considering he only started one game at the Euros, I thought he did well.
"Make no mistake, he is a very good footballer. I can fully understand why Newcastle are in for him and I think it would be a great move.
"When he was there before he benefited from the fact that the team was always working to get him the ball - and he thrived on that. That hasn't always been the case at Liverpool and perhaps at times he suffered."
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He added: "There is an old saying that you should never go back but, in Andy's case, I don't think it would be a mistake at all.
"He was hero-worshipped by the crowd first time around and they would warm to him again. Andy loved playing there and whatever the fans felt about him leaving to join Liverpool, I'm sure he would win them over quickly."Carroll has also been linked with a move to recently promoted West Ham and Serie A runners-up AC Milan.