The pair will go head-to-head on Saturday in the El Clasico at the Santiago Bernabeu.
And Diario Gol says Ronaldo holds a personal grudge against Suarez, who he can't stand for his on-field behaviour.
While the mutual respect for Lionel Messi is rock solid, the same cannot be said for Suarez.
Ronaldo finds his antics during the game trying, with it claimed Suarez is always swearing at the opposition and match officials and regularly getting in the face of defenders.
However, there is also some jealousy. Ronaldo resents the way Suarez is forever supportive of Messi on the field, sacrificing his own game to help the Argentine score. This is in contrast, Ronaldo feels, to some of his younger teammates who he believes have ignored him in excellent scoring positions this season.
Suarez, meanwhile, was quick to dismiss Ronaldo's demand of a guard of honour from Barca's players after Real's Club World Cup triumph.
"That guard of honour is a new thing for me since arriving in Spain," the Uruguayan said.
"I know it is said that in the rules if you are also in that competition which your opponent won, then you do it as a sign of respect.
"But on this occasion, we had nothing to do with the Club World Cup so we don't have to do it. That's the decision the club made."