Del Piero, who scored 290 goals in 705 appearances for Juve between 1993 and 2012, told La Gazzetta dello Sport that there had been contact with the Hoops as his time in Serie A came to an end.
He said: “When I left Juventus, I had the chance to join Celtic - but I rejected their offer because I didn’t want to play for another team in Europe.
“I had already decided to leave the continent.”
Del Piero later joined Sydney FC in Australia, before a brief spell with Delhi Dynamos in India.
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He continued: “In the following season, Juve and Celtic met in the Champions league and I thought, ‘luckily I didn’t join them!’”
The 91-times capped Italian forward pointed out that another Juventus hero, Gianluigi Buffon, risks a similar scenario having joined Paris Saint-Germain this summer.
The 43-year-old added: “If it’s going to happen, it will be Gigi’s business... I’m joking! I will follow Gigi in Paris but if he had to face Juve in the Champions League I couldn’t support him.”
Del Piero, who occasionally provides analysis on Sky Sports Italia, faced Celtic with Juventus in 2001. Naturally, the Italian striker scored for Juventus in a 4-3 win for Celtic at Parkhead in October 2001.