According to talkSPORT, the Magpies made Cole an offer in the final hours of the summer window, but he spurned the chance to seal a reunion with England’s top flight.
He has just one-year remaining on his Roma contract, and the report claims that the Serie A outfit will not offer him an extension.
He is expected to leave in January.
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Cole made just 11 appearances in Italy last season, and could be considering retirement at the age of 34.