The 23-year-old scored the only goal in United's 1-0 win over Lyon at Old Trafford, to ease the Premier League holders into the last eight, 2-1 on aggregate.
"I would prefer to play a foreign team [in the quarter finals]. Then an English team in the semi-finals or the finals, that would be fantastic," he told reporters after the game.
"The team is more mature, and the big focus is to win the Champions League. But we also want to win the Premier League, and the FA Cup. We have the opportunity, we have the players and we have the squad."
Ronaldo has netted six goals in the Champions League this season, and is a good bet to be top scorer this season in the competition.
However, the Portugal winger has played down the lure of personal milestones and insisted that he is just concentrating on making Sir Alex Ferguson's starting eleven.
"If I am top scorer, that would be wonderful, and if I get the chance, I will look forward to it. But, I am not thinking about that - I am thinking about getting my game."