Cayzac tendered his resignation following a meeting on Sunday with Sebastien Bazin, a representative of PSG's main shareholder, Colony Capital, and coach Paul Le Guen.
PSG have now appointed Michel Moulin as director of sport but Ceyzac told French newspaper L'Equipe he wanted Mourinho for the job.
"I thought about approaching Jose Mourinho," he said. "I had been in touch with him, he was out of the job and wasn't looking for an enormous amount of money. We made contact but it was too late."