Rice scored the only goal of the game on Saturday as West Ham recorded a 1-0 win over Arsenal at The London Stadium - their first home win over the Gunners in 13 years.
The 20-year-old curled home a wonderful first-time finish inside the box on 48 minutes.
It was a solid performance overall from one of Europe's brightest young defensive midfielders, who Chelsea released as a 14-year-old.
But Redknapp believes that it won't be long for the Premier League's elite to take an interest in the England-born star if he maintains this standard.
"Rice read the game superbly, picked pockets throughout and made some crucial blocks. His winning goal was the icing on the cake," he told The Daily Mail.
"After the ball rifled into the Arsenal net, you could see the joy written all over his face. All the heartache, all the disappointment that led to this moment will have made it all the sweeter.
"It was a privilege to be at the London Stadium to witness his maiden strike. Keep up these brilliant displays and the Premier League's top sides will start circling."
Redknapp is right in saying that bigger clubs than West Ham will circle eventually, but the Hammers made a brilliant pre-emptive decision in signing him up to a new long-term deal last month.
That will keep the wolves from the door for a while at least and ensure that if he does move on, it'll be for a lot of money.
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