The Tyneside club's manager Alan Pardew would not be drawn on whether or not he would attempt to re-sign the striker, following comments from new Liverpool boss Brendan Rodgers, who suggested Carroll might benefit from a spell away from Anfield.
But, according to various reports, Newcastle are interested in a return for the 23-year-old they sold to Liverpool during the 2011 January transfer window.
Rodgers' comments, and the signing of Italian striker Fabio Borini from Roma have fuelled speculation linking Carroll with a departure from Merseyside.
Carroll has been linked to several clubs over the summer, including AC Milan and West Ham, with Hammers co-owner David Gold suggesting the Londoners would not rule out a bid.
Aston Villa boss Paul Lambert, meanwhile, also refused to dismiss the possibility of signing Carroll, should the England international become available.
Newcastle boss Pardew would only back Carroll when quizzed on interest in bringing the £35 million man back to the club.
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"He did an absolutely terrific job here," Pardew said. "I have always supported him while he has been at Liverpool when other people weren't. I thought he got a bit of a raw deal, if I'm honest.
"I think he's going to be a great player, but where he treads the boards, so to speak, we will have to wait and see."