Balzaretti performed at both left-back and right-back for Italy as they reached the final, only to lose 4-0 to Spain, and caught the eye with his performances during the finals in Poland and Ukraine.
Both Napoli and Milan have been linked with the 30-year-old but he says he will only consider staying at Palermo or moving to PSG, who are managed by an Italian in Carlo Ancelotti.
“I’ve already spoken to the president and told him of my priorities,” he told the Corriere dello Sport.
“I’ll either stay at Palermo or move to Paris Saint-Germain – there are no other solutions.”
PSG entered the Italian market on Monday when signing Napoli forward Ezequiel Lavezzi for a reported fee of 30 million euros.
Meanwhile, Palermo have confirmed the sale of Mattia Cassani and Mauricio Pinilla to Fiorentina and Cagliari respectively.