Giggs, who played alongside Ronaldo at United when he lifted the first of his five Champions League titles, believes a desire to conquer Italy may stem from his former team-mate's need to be the best.
"I'm surprised that he would leave Real Madrid and go to Italy," Giggs said on ITV.
"I think it's a big challenge for him but he's going to a huge club. Having that on your CV: Real Madrid, Man United, Juventus - it's some CV.
RT @OptaJavier 0 - Lionel Messi #ARG and Cristiano Ronaldo #POR have never scored in the knockout stages of the World Cup; between both of them, they accumulated 1.270 minutes without scoring (756 Messi, 514 Ronaldo). Era. pic.twitter.com/LbGzt3PEjy— OptaJose (@OptaJose) June 30, 2018
"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?'"