The Scottish Premiership side ultimately decided against signing the Dutchman, instead going for another striker.
Davie Hay has explained how Celtic were weighing up a potential move for Michael Mols just a few years before the Dutch striker completed a move to their bitter rivals Rangers, the Evening Times reports.
Mols would go on to win three Scottish Premiership titles, two Scottish Cups, two League Cups and score the winning goal in an Old Firm contest in 2002.
But Hay has explained how close he came to becoming a Hoops player several years before he did move to Glasgow.
"I felt that van Hooijdonk had more goals in him, while Mols was better at leading the line.
"It was one of those occasions when all three of us - Tommy, myself and Billy - went to watch them both play before deciding that it was Pierre that we would go for."
The decision to sign Mols' countryman instead was seemingly vindicated instantly as he scored the only goal in the 1995 Scottish Cup final just months after moving to Parkhead.
And while van Hooijdonk's time with the Bhoys would ultimately end in acrimonious fashion, he did prove to be lethal in front of goal, scoring 44 times in 69 league games for the team before leaving for Nottingham Forest in 1997.
But while van Hooijdonk was prolific during his time in Scotland, the fact that Mols was able to help his side win more silverware during his time with the Light Blues would suggest that Hay and Tommy Burns perhaps made the wrong decision in leaving the path clear for their rivals to swoop in several years later.