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The actor was the first choice to star opposite Olivia Newton-John in the smash-hit musical, but decided to pass in case he became typecast in "cool guy" roles.
But he now regrets the decision because his replacement John Travolta went on to be a Hollywood star, while he failed to find success after playing the Fonz.
He said: "I was asked to be in Grease. But I decided I didn't want to be typecast. But what I didn't realise was that I already was.
"That's why John Travolta went on to buy his own plane and I just went home."
Winkler recently claimed that 24 character Jack Bauer is a modern replacement for the Fonz.
> Digital Spy examines why Grease has remained popular for over three decades
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