Del Piero is expected to leave the club in 2012 after being informed by president Andrea Agnelli that he has no future with the Old Lady.
Giovinco has been touted as a replacement for the 36-year-old Italian, while Juventus general director Giuseppe Marotta said the club are keen on taking him back from the current co-ownership agreement with Parma.
However, Parma CEO Pietro Leonardi is in no mood to allow the 24-year-old to return to Turin.
Giovinco, though, has other ideas, but, like many critics, he has questioned the wisdom of Juve dumping Del Piero.
"Alex represented, and still represents Juventus. He is the club's history maker, but perhaps Juventus mistimed the situation," Giovinco told Sky Sport Italia.
"Me the new Juventus No. 10? For now I am thinking about my No. 10 with Parma. If the clubs agree in future we will see."
Giovinco's previous spell with the Turin club ended acrimoniously, but he no longer harbours ill feeling towards the giants.
"The anger against Juventus has passed now as I am having one of the best moment's of my career," he said.
"I do not want to think about negative things."