The Reds flatly turned down the Magpies' bid to re-sign the 23-year-old international on a season-long loan over the weekend, but have made it known they would be willing to listen to offers for a permanent transfer for a player who cost them £35million 18 months ago.
And Shearer reckons heading back to the North-East could be the best option for Carroll.
The 41-year-old said in 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."
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."
Liverpool jetted off on their North American pre-season tour on Monday - Carroll is due to join them early next week after an extended holiday.
Sources close to the player have indicated that he remains keen to prove himself at Anfield despite new manager Brendan Rodgers' misgivings, although he would entertain the right loan move.
Newcastle would fit the bill - Gateshead-born Carroll made his name at St James' Park after emerging from the ranks to establish himself as a genuine first-teamer under former boss Chris Hughton, and is understood to prefer a return rather than a mooted move to West Ham or AC Milan.
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