The former Manchester United hitman is widely expected to leave the Bernabeu after finding his chances limited under current Real boss Manuel Pellegrini.
Van Nistelrooy netted over 150 goals during his time at Old Trafford and Redknapp is confident the 33-year-old would be a huge success should he return to England.
And the Spurs boss also admitted he wouldn’t be surprised if the Dutchman joined rivals Arsenal.
“He’s a top player. If he’s anywhere near fit I’m sure he can still play for a while but I’ve never enquired for him," Redknapp told the Press Association.
“I can see him going somewhere like Arsenal.”
Van Nistelrooy has been hampered by injuries during the past year and has made just one La Liga appearance so far this season.
Redknapp revealed he is a big admirer of the much-travelled frontman but is adamant he has more than enough fire-power amongst his current crop of strikers.
Spurs are the third highest scorers in the league after netting 35 goals in their opening 16 games, and the 62-year-old has no plans to alter his attacking line-up in January.
“Tottenham is a big club, we shouldn’t be afraid to compete with these clubs in the transfer market," he said.
“But what would I do? I have [Peter] Crouch, [Robbie] Keane, [Jermain] Defoe and [Roman Pavlyuchenko] ‘Pav’.
“If I got Van Nistelrooy, I give myself another problem.”
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