However, he insisted that there is no need to compare them, as they are both great players.
“For me, this fight doesn’t exist,” Ronaldo told reporters after Chinese publication, Dongqiudi, named him their 2016 best player.
“You can’t compare players. Cristiano is Cristiano and Messi is Messi,” Ronaldo replied reporters.
“We are both great players with individual and team titles that speak for themselves. The comparison? I don’t like to compare, that word doesn’t exist for me. We are different, two people just doing their jobs, that is all.”
Ronaldo insists both players have mutual respect for each other.
He said: “He tries to be the best player for his team and I try to do the same for mine. We are rivals because we play for different clubs, but when we are together we show each other mutual respect. We have a normal relationship.
“People compare us all that time, that is normal. People even compared our sons when they were born and talk about who is the fastest and smartest at school. This is all part of the business. But I think that you can’t compare these things.”
The Portugal captain added: “I just don’t care about [my critics]. I try to do my job and be myself, everyone has people who hates them and it’s part of the business.
“But, I go to bed happy every night, I’m not here to satisfy my critics as I’m here for my fans and those who make me happy.”