However, Juventus forward Ronaldo, who was also part of Madrid's Champions League-winning team, felt his Ballon d'Or case was even stronger.
Ronaldo and Messi had shared the Ballon d'Or between them for a decade before Luka Modric broke their duopoly last week, with Messi also finishing ahead of Ronaldo in the ESPN FC 100.
" I'd like him to come to Italy one day. I hope he accepts the challenge like me, but if he's happy there then I respect that", Ronaldo told the Italian press.
"Maybe I miss him a little. I have played in England, Spain, Italy, Portugal, with the national team, while he has stayed in Spain".
Ronaldo added: "If he is happy there, I respect him". Do what I did, accept the challenge. Marcelo is great, the doors are open for the great player and Marcelo is one of them.
"This is my new life and I'm happy".
"If I played against Real, I would try to give my best". For me it is lovely, to feel that difference.
Ronaldo says he is absolutely convinced he made the right decision to leave Real Madrid for Turin in the summer but admits different clubs were interested in signing him.
"The past has passed and now I want to win for Juventus", he said.
"This is not a contest between me and Messi - I just do my job and I've been successful in each club I've played in and this is the most important thing".
Ronaldo has already struck 11 times and assisted a further seven strikes in 19 matches across all competitions for Juve this season.
Juventus are next in action on Wednesday when they conclude their Group H Champions League commitments away to Young Boys.
"The Champions League can not be an obsession, you have to think about it calmly", he warned.
"Look at the game against Manchester United (2-1 defeat), if it had been a quarter-final we would have gone out".
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