Keegan was England's star man going into the tournament in Spain 35 years ago, but injuries to him and Trevor Brooking scuppered their dreams of glory.
Kane and his Tottenham team-mate Dele Alli are probably the modern-day equivalent of Keegan and Brooking, and the former England captain and manager has warned it is vital they stay fit for next summer's finals in Russia.
"I did think we had a chance in 1982 until me and Trevor Brooking got injured," he recalled. "We had other good players, but we were the main reason we qualified.
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"It's important everyone stays fit. Not just Kane, but also Dele Alli. You want all your best players, and then you have got a chance.
"If you went to a World Cup and you took, let's say, Johan Cruyff and Johan Neeskens out of the great Dutch side, people would not be surprised if they lost.
"But with England, people still think you are going to win it without your two best players. It's being English, it's the optimism."Kane's goal against Slovenia rubber-stamped England's qualification for Russia next year at the end of a dismal match, which Keegan wisely missed in favour of a wine-tasting evening.Nevertheless, Keegan admits he has been won over by the Spurs frontman having initially had his doubts.
"Alan Shearer is a massive fan of Kane," added Keegan, speaking at the Aspire Academy event.
"I know from when I worked in Qatar with him he was saying how good Kane was. That was a year and a half ago and I wasn't sure.
"I said we need to have a good look at him, see if he gets the 20 or 30 goals that you were getting - and of course now he is doing that."