Fitzpatrick was St Mirren skipper when the 19-year-old Clarke burst onto the scene with the Paisley club in 1982 as a talented young defender.
After more than 200 run-outs for the Buddies, boyhood favourites Celtic had seen enough to make their move.
But the Saints board turned down the Hoops' bid as they refused to deal with one of their domestic rivals.
The collapse of his Celtic switch left the full-back heartbroken but he refused to sulk and eventually won a £422,000 move to Chelsea in 1987.
During an 11-year Stamford Bridge career, he would win the FA Cup, League Cup and European Cup Winners' Cup.
Now Fitzpatrick believes that steely resolve will help the 50-year-old succeed if he is chosen to replace Neil Lennon as the Scottish champions' new manager.
He said: "Stevie is a Celtic fan. I remember when Davie Hay was in charge of Celtic, they came in for him but St Mirren - who were challenging for Europe around that time - would not sell to another Scottish club.
"So he ended up going to Chelsea, where he became a legend.
"Stevie had been desperate to go to Celtic but it's a mark of the man that he never threw the toys out of the pram. He dealt with it brilliantly and it shows his mental toughness that he was able to put that disappointment behind him and do so well at Stamford Bridge.
"That's exactly the type of thing you need if you are going to be a successful Celtic manager."
Fitzpatrick has watched the former West Brom boss's career with interest since their Love Street days and always knew he would go on to manage at the highest level.
"Stevie is a winner and you could see that from the day he walked into the St Mirren dressing room as a young player," said Fitzpatrick. "He was always very focused.
"In terms of his stature, he was right up there with all the big Saints players of the time - Frank McGarvey, Frank McAvennie, Billy Stark, Peter Weir.
"He was just so determined to be a top player and he had a real steeliness about him, that mental toughness.
"From an early age you could tell he would go on to become a manager too. He was a student of the game and always hungry for knowledge about his position and how the team should play."
Clarke became the bookies' favourite to land the Hoops post after former Manchester United skipper Roy Keane pulled out of the running on Monday.
He started his coaching career as assistant to Ruud Gullit at Newcastle before helping Jose Mourinho land two Barclays Premier League titles after returning to Chelsea.
He also had spells as number two to former West Ham boss Gianfranco Zola and Kenny Dalglish during his second stint as Liverpool manager.
But his sole venture as a boss in his own right ended after less than 18 months when he was axed by West Brom in November last year, despite leading the Baggies to eighth place in his first season in charge.
"I really hope he gets this chance because he deserves it," said Fitzpatrick. "He's a phenomenal guy.
"Just look at the experience he has had and who he has worked under. Gullit, Mourinho, Zola, Dalglish - these guys are from a different planet.
"You also have to look at how well those clubs did during his time there. Stevie played a huge part in their successes.
"If you listen to the way Mourinho talks about him, you realise just how special a coach he is.
"I was surprised the way things worked out for him at West Brom, though, because I thought he did a great job. That would have hurt him, especially because he was doing well - but it will have made him even more hungry to succeed.
"Now, he's more than ready for the Celtic job and I'm sure he would make a great appointment."