The Bournemouth midfielder, 21, has started every game in the Premier League this year.
His maturity at such a young age has raised interest from the big clubs in England, and Redknapp believes Cook is "destined" to play at the top level.
"Lewis Cook may have made a mistake for Tottenham's third goal but that should not take away from what was a brilliant performance," he told the Daily Mail.
"He has been on my radar since his days at Leeds but he has come on leaps and bounds at Bournemouth.
"In a year or so I am in little doubt he will get a chance to play for one of the big six sides. This boy is destined for the top."