Portsmouth have released five players but offered a new contract to veteran Nigeria international Kanu and could still tempt Sol Campbell to remain at Fratton Park.
Noe Pamarot, Lauren, Glen Little, Djimi Traore and Jerome Thomas have all been told their futures lie away from the club after their contracts expired on June 30.
Executive chairman Peter Storrie told Pompey's official website: "Kanu has the option of another year, which he's considering.
"There aren't any discussions going on with Sol (Campbell) at the moment. In terms of whether there will be further discussions, we'll look at it next week."
Pamarot, Little, Thomas, Lauren and Traore all struggled to break in to Portsmouth's first team last season and were periphery figures in the closing weeks of the campaign as Paul Hart guided the club away from the bottom three.
Jermaine Pennant, Pele, Armand Traore and Theofanis Gekas have already left the club after spending time on loan at Pompey last term, while Glen Johnson has signed for Liverpool and Sean Davis has agreed a three-year contract with Bolton Wanderers.
Meanwhile, Arnold Mvuemba is training with French side Lorient ahead of a possible transfer.