A life-long supporter of the Glasgow side, Clarke was once pursued to sign for them after impressing during a spell with St Mirren. Fitzpatrick had been captain of the Paisley side when the defender burst on to the scene in 1982 and was well aware of what the move would mean to him.
St Mirren proved unwilling to do a deal with a domestic rival and Clarke was instead left to overcome his disappointment and instead transfer to Chelsea. The Scot moved to London in 1987 for a fee of £422,000 - winning the FA Cup, League Cup and European Cup Winners' Cup during an 11-year spell.
It is that strength of character as much as his coaching credentials which could allow Clarke to succeed as manager of the Scottish champions. The former West Bromwich Albion head coach became the favourite for the role after Roy Keane ruled himself out of contention.
"Stevie is a Celtic fan," said Fitzpatrick. "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.
"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."