The 24-year-old endured a difficult first season at Liverpool after completing a record £35m move to Anfield from St James’ Park in January 2011.
Despite managing just two goals in 11 appearances in an injury-hit spell at the Hammers, the east London club have already agreed a deal with Liverpool for the striker.
But Newcastle managing director Llambias hinted the Toon would be interested in re-signing Carroll if the opportunity arose.
“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 11 goals in 58 appearances for the Merseyside outfit since his club record move.