Lewandowski, 24, scored each of Borussia Dortmund's goals in the first leg of their Champions League semi-final as the Germans thumped their Spanish counterparts 4-1 ahead of next Tuesday's reverse fixture in Madrid.
The Polish striker - the first man to hit a Champions League hat-trick against Los Blancos - is only contracted to Dortmund until the summer of 2014, and Sky Sports pundit Redknapp reckons European football's elite will now try to prise him from the Westfalenstadion.
"Lewandowski has introduced himself to the world," said the former Liverpool midfielder. "People in Europe knew all about him but he showed tonight [Wednesday] the quality he has in his all-round game.
"He produced one of the best individual performances I've seen in such a long time; he led the line, was the focal point of the team, got his head up and brought other players into play, and finished.
"He was absolutely different class and proved to anyone who thought that he might not have it all that he is the real deal - and as he is out of contract next season he is definitely going somewhere.
"Manchester United were apparently looking at him but I think every top club in Europe will want to see him because he is a top footballer who delivered an absolute exhibition of how to play as a No. 9 [against Real]."
Redknapp's fellow analyst Graeme Souness added: "Lewandowski is a very clever footballer, as well as having all the technique you will ever need, and he will be an asset to anyone.
"He has got a lot of everything - the goals, the build-up play, the ability to back in and go where you might get hurt - and, given his age, he might have eight years at the top level."
Souness believes Dortmund's domination of Madrid in front of their vociferous home fans will go down as one of the "great nights of European football."
And even though he thinks the 2011 and 2012 Bundesliga champions will be tested in the second leg in Spain, he expects Jurgen Klopp's charges to book their spot in May's final at Wembley.
"It has been an absolute privilege to be [at Signal Iduna Park] for one of the great nights of European football," said the Scot, who won the European Cup with Liverpool in 1978, '81 and '84. "The supporters didn't stop all night and the team effort from Dortmund was as good as it gets.
"There was a period with about 25 minutes on the clock when Madrid started to get a foothold but they were really not that threatening.
"Cristiano Ronaldo had one of the quietest games I've seen him play and it was the right result as Dortmund were scary for 90 minutes.
"I think that is as good as it gets for Dortmund, though; I don't want to pour cold water on them but there must be a chink somewhere because they have conceded 35 goals in 30 games in the Bundesliga this season - but I think it is a mountain too high for Madrid."
Redknapp added: "Dortmund are a wonderful young side. They won every second ball, closed down and pressed; they made life so difficult for Real and, at times, made them look old, clumsy and pedestrian.
"Can I see this Dortmund side not scoring in Madrid? No. They have so much quality and pace and you feel the more Real push at home the more spaces they will leave at the back."