Adams wants to bring in the Ivory Coast star as a replacement for Lassana Diarra, who looks set to join Real Madrid.
It is not believed that Spurs boss Harry Redknapp is to interested in selling the former St Etienne ace in January, but a £10million bid could make him change his mind.
A Fratton Park insider told News of the World: “Tony has let it be known that he wants Zokora and he’ll be ringing his old boss Harry in a bid to try and thrash out a deal.”