The 22-year-old has struggled to rediscover his best form since making his £35million move to Merseyside last January, and is said to be willing to return to the North East.
Magpies boss Alan Pardew is a huge admirer of the former Newcastle hitman, and has always left the door open for Carroll to return to St James' Park.
"You never want to lose great players and we never wanted to lose Andy," he said. "I'd take him back if I had the chance.
"If the fee offered by Liverpool had not been so high, he'd still be here."
With just five goals to his name since making his move to Anfield, Carroll has grown increasingly frustrated, despite receiving backing from Reds boss Kenny Dalglish that he will return to his best.
However, a loan move back to Newcastle may benefit both parties, with Pardew short on striking options, as top goalscorer Demba Ba prepares to leave for African Cup of Nations duty, and Liverpool linked with a big-money move for Darren Bent.