Ronaldo left Real Madrid after nine successful seasons, where he won the UEFA Champions League four times.
He is now with Juventus, the Italian champions, where he will spend the next four seasons.
"I'm surprised that he would leave Real Madrid and go to Italy," Giggs said on ITV.
"He's obsessed with being better than Messi. He has that now, that, 'I did it in England, I did it in Spain, I'm going to do it in Italy ... I did it with Portugal.'
"So maybe that will be his argument when [he asks himself]: 'Am I better than Messi?'"