The 24-year-old left St James' Park in a £35m deal to Liverpool in January 2011, but is currently on loan at West Ham United after reportedly being told that he does not have a future at Anfield by new manager Brendan Rodgers.
The Magpies made an offer to take Carroll on loan in the summer, but were outbid by the Hammers, who have a £17m option on him at the end of the season.
However, Llambias has hinted that another move could be in the pipeline should the opportunity arise.
"We've always had a bit of a soft spot for Andy here," Llambias told the Newcastle Chronicle. "He's a character and he's getting older and more mature – and he's stronger.
"It's unlucky what has happened at West Ham, but he scored a great goal at the weekend. He's still got a house up here. Andy was part and parcel of our growth."
Carroll has scored two goals in 12 appearances this season.