The Daily Mail says boss Harry Redknapp was keen to be reunited with his former West Ham striker and could land the Mali international for around £7million.
However he said recently he is adamant he will stay at Spurs to battle for his place despite the arrival of Darren Bent from Charlton for a club record fee.
Redknapp admits he would welcome the striker at Fratton Park if the situation changes.
"I've love Defoe or Kanoute," said Redknapp said. "Defoe is a fantastic player in my opinion.
"He needs to play. Spurs are so strong up front. Robbie Keane is a magnificent players, there is Berbatov and they took Bent.
"I gave Jermain his debut at West Ham and I know the kid - he loves playing football and loves scoring goals. He needs to play somewhere."