The coach's representative says the French giants lost interest after learning of the circumstances surrounding his potential contract release from Russia
Negotiations between both parties were said to be at an advanced stage after the 67-year-old met with sporting director Leonardo in the French capital on Wednesday.
However, Pierfilippo Capello - who acts as his father's agent - says the Ligue 1 champions were put off the idea of appointing the Italian but insists the ex-Real Madrid and England coach did not reject les Parisiens.
"PSG asked under what conditions Fabio could leave his job with Russia. I cannot reveal what those conditions were, but I can tell you that they were not suitable for PSG," he told RMC Sport.
"Once everybody understood that they were not happy with the conditions of his release from Russia, the talks did not go any further.
"Fabio Capello did not say 'no' to them. There was no reason to say yes or no because there was no offer from PSG for him.
"As his representative they have never asked me if Capello was interested in quitting Russia to become their coach because we did not get that far.
"I explained the conditions with which Fabio could leave his role with Russia and they told me that it did not suit them and we stopped there."
The former Juventus coach is contracted to the national team until 2014, after signing a lucrative two-year deal in 2012.