Ronaldo moved to Juve in the close season for a fee of €112 million (£100.7m/$127.5m), ending a nine-year stint at Real Madrid, and his agent Mendes said on Saturday that the move was the forward's idea.
And Paratici has now backed up that version of events, despite previous claims that Ronaldo had been forced out of Madrid after failing to agree a new contract at the end of the 2017-18 campaign.
"When we met with Mendes to discuss Cancelo, that is where the whole thing began," Paratici told Sky Sport Italia.
"Mendes said to me: 'You won't believe this, but Cristiano wants to come to Juve.'
"I replied that I believed it, but it seemed difficult to make everything come together and work."
Ronaldo has hit his stride in Turin, and has scored 12 times in all competitions to help Juve move clear at the top of Serie A and progress in the Champions League.
But Paratici added that bringing in the Portugal star never seemed a likely option.
"The greatest players help kids to dream. My son wanted Cristiano Ronaldo's jersey, so when I went to see a Portugal game, I bought it and he wore it all the time.
"Every year he'd ask me: 'Daddy, why don't we buy Cristiano Ronaldo?' Because it's impossible.
"Then when it happened, he said: 'Daddy, you told me it was impossible!' I had no answer."
Juve secured a 1-0 victory over Roma on Saturday, ensuring Massimiliano Allegri's side have an eight-point lead over second-placed Napoli and have now won 16 of their 17 league fixtures this term, only dropping points in a 1-1 draw with Genoa.