Carroll’s contract at St James’s Park expired at the end of last month along with those of Christian Atsu and Henri Saivet.
And the striker is now searching for a new club, according to The Times, after being told he will not be offered a new deal.
Carroll – who returned to Newcastle two years ago as a free agent after leaving West Ham United following the expiry of his deal at the London Stadium – had signed a 12-month extension last summer.
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The 32-year-old made four starts – and 14 substitute appearances – in the Premier League last season. The only goal of Gateshead-born Carroll’s second spell at United came in a 2-1 defeat to Leicester City in January. Carroll had originally left the club in January 2011 and joined Liverpool in a £35million deal.