The 33-year-old brought down the curtain on his nine-year spell at the Bernabeu on Tuesday afternoon after agreeing to join the Serie A champions in a nine-figure transfer.
Ronaldo has also starred in the Premier League with Manchester United, where he spent time playing alongside Giggs, and his former teammates believes that an 'obsession' to prove himself as the world's best could be behind his latest move.
"I'm surprised that he would leave Real Madrid and go to Italy," he told ITV Sport. "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 and Juventus. It's some CV.
"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... and I did it with Portugal'. So maybe that will be his argument when people ask: 'Is Ronaldo better than Messi?'."
Ronaldo won two La Liga titles, two Copas del Rey and four Champions Leagues during his time in the Spanish capital.