The Portuguese has found the net eight times in just four European appearances this season to equal the record jointly held by Ruud Van Nistelrooy, Filippo Inzaghi, Hernan Crespo and Zlatan Ibrahimovic, who has also scored eight times for Paris Saint-Germain this season.
Ronaldo has missed Madrid's last three games due to a slight muscular injury and suspension respectively, but Madrid boss Carlo Ancelotti confirmed that he will return in midweek despite Madrid having already sealed their place in the last 16.
"Cristiano is fine, he is training with the rest of the team and he will play on Tuesday without any problem," said the Italian.
And despite a lot of talk surrounding what he may do at the World Cup next summer, Ronaldo insisted his primary focus is on delivering trophies for Madrid before making his way to Brazil.
"There's still a long way to go to the World Cup and I am focused on my club. I want to win everything and then we'll see about the World Cup," he said. (2014 FIFA World Cup draw)
"We have to enjoy the present, right now we are playing well in the Champions League, La Liga and now the Copa del Rey.
"I hope Madrid can win something important. There is sill a long way to go until the World Cup and anything could happen. My aim is to stay focused on my club and give my best."
Gareth Bale is also expected to return in the Danish capital as he trained alongside Ronaldo on Sunday despite missing Real's 0-0 draw away to third tier Olimpic Xativa in the first-leg of their Copa del Rey tie on Saturday due to the flu.
Copenhagen cannot make the last 16 no matter how results on Tuesday go due to their inferior head-to-head record against Galatasaray and Juventus.
However, Stale Solbakken's men can still make the Europa League with a win or by bettering Galatasaray's result at home to Juve.
And after a group stage in which his side have competed well against opponents with vastly greater resources, Solbakken is hoping for another stellar home performance to ensure European football after Christmas.
"We are still alive and we will hope that we can provide one last, brave effort to go through (to the Europa League)," he told the club's website.
"I have said that I hope for one Christmas present before December 24 and that is a win or maybe a draw at the Parken."