Spurs have since appointed Juande Ramos from Sevilla as their new head coach and Redknapp said: "There wasn't really any truth in the Tottenham rumours.
"I enjoy looking forward to going to work every day. Life's good here and it never entered my mind to want to leave here. I'm very happy here."
But the Pompey boss still believes Tottenham can finish in the top seven of the Barclays Premier League even though they currently sit third from bottom.
Redknapp said: "After the top four, there are eight clubs who could finish fifth, sixth, seventh and eighth.
"Tottenham can put a run together and have got probably the best squad outside the top four - they could finish in the top six or seven.
"If we can stay in the top half all season, we will be very pleased. We've got a good backroom staff, fans and players - the club's in good shape at present."