Busby's team would go on to lift the trophy at Wembley after defeating Eusebio's Benfica 4-1, just 10 years after the nightmare of Munich.
Whether United would have challenged Real's dominance of European football during the 1950s remains a hypothetical question.
Real signed one of the greatest players to have ever stepped onto a football field in the shape of Hungary's Ferenc Puskas in 1958 and saw off all comers until a Bela Guttmann-inspired Benfica broke the stranglehold in 1961.
"Would the Madrid team have remained so dominant in Europe had Munich not happened? I don't think that they would," said Clare.
"I think that United were on course to win the European Cup in 1958. They were such a young vibrant team, who had gained their first season of experience in Europe and had learned a lot from it.
"There was also much more strength in depth at Old Trafford than there was in Madrid.
"People forget that in season 1958-59, just months after the tragedy, United's patched-up young team finished runners-up in Division One to champions Wolves -- that was some achievement."
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