The Greece international was put on the transfer list last week after falling out of the first team reckoning following the arrival of Jonathan Woodgate, and expressing an interest in leaving St James’ Park.
Pompey boss Harry Redknapp has confirmed he is keen to sign the player, telling the Daily Telegraph: "Nikos has got a lot of experience at the very highest level and we need that if we're to survive in the Premiership."
Manchester City, Charlton Athletic and Everton are amongst the other Premiership clubs rumoured to be keen on signing Dabizas, with his former club Olympiakos also believed to be interested.