The Sun says Redknapp is still trying to persuade Van Nistelrooy to return to England three years after leaving Manchester United.
Spurs would have to break their strict wage structure to lure the veteran striker to White Hart Lane and the club have adopted a recent policy of signing younger players with a high resale value.
Van Nistelrooy, 32, has not played since undergoing a serious knee operation last November.
But Redknapp believes landing the prolific Holland ace for a cut-price fee would be a massive coup for the club. Van Nistelrooy remains unconvinced and is tempted to see out the final year of his £100,000-a-week contract at the Bernabeu despite being told he can leave.