Jose Mourinho's team have been lifted by Ronaldo's 21 goals - exactly half his amazing haul for Manchester United in 2007/08 when the England club claimed the European title - and that alone should give their fans reason to be optimistic.
The La Liga giants have failed to advance beyond the Champions League last 16 the past six seasons despite huge investment in players and they are still smarting from last month's 5-0 thrashing at Barcelona.
But having topped Group G with five wins and a draw, scoring 15 goals and only conceding two to complete their best-ever performance in the group phase, Real look to have a good chance of winning the trophy for the 10th time.
"I am confident we will be fighting to the very end in every competition," Ronaldo told reporters after scoring his fourth goal of the European campaign in Wednesday's 4-0 demolition of Auxerre.
"I love being a part of the game; making assists and scoring. I always celebrate goals with my team mates," added the Portuguese forward, whom Real made the world's most expensive player when they lured him from Manchester United.
Atletico Madrid central defender and Uruguay international Diego Godin said Ronaldo's strength made him a particular handful.
"He has tremendous confidence in his speed and in his technique," Godin told don Balon magazine. "He has ambition and is a born goalscorer.
"He is different (from Barcelona forward Lionel Messi) in that he is more predictable, although he is so strong that even then he can beat you."
This will be music to Mourinho's ears as he strives to become the first manager to win the Champions League with three clubs.
It should be a warning for Real's possible last-16 opponents Inter Milan, the holders from whom they poached Mourinho at the end of last season, and 2006 finalists Arsenal, who were both second in their groups.
Other possible opponents include AS Roma, who knocked them out at the last 16 in the 2007/08 competition, and Olympique Lyon, who scuppered the Spanish giants' campaign at the same stage last season.
