The Spanish giants currently sit top of the Primera Division table with 34 points from 13 games, while they qualified for the knockout stages of the Champions League from Group D without dropping any points.
Ronaldo is hopeful they can keep up their good form, but declined to give his opinion on whether Jose Mourinho's side have finally caught up to Barcelona.
"I can't say whether Real Madrid and Barcelona are of the same level or whether Madrid play even better than Barca. I can only say that I hope Madrid win La Liga and the Champions League, and beat Barcelona as well," Ronaldo said to AS.
"I try to follow La Liga as closely as possible. I didn't have the chance to see the derby, but I know that Madrid won and are in great form. I think that they can achieve great things this season."
Ronaldo wore the Real Madrid jersey from 2002 until 2006 and won one league title as well as the Intercontinental Cup and the Spanish Supercup during his time at the Santiago Bernabeu.
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