Stale Solbakken's men can seal a Europa League place with three points on Tuesday as Ronaldo prepares to make his comeback from injury.
The visitors to Parken head into the game having already secured top spot in Group B. Indeed, Los Blancos have dropped just two points, away to Juventus, but could well face a stern test against a side that has not tasted defeat in either of its previous home games in the competition.
A 3-1 defeat in Turin ended Copenhagen’s hopes of reaching the last 16, but the Danish outfit can still earn a berth in the Europa League.
A win would guarantee Stale Solbakken's side third place, while a draw would be enough if Galatasaray is beaten at home by Juventus.
Copenhagen will have to improve markedly on its performance at Santiago Bernabeu in October, though, when it was routed 4-0 by Madrid.
Cristiano Ronaldo and Angel Di Maria both scored twice in that game, and the former is in line to torment Copenhagen again as he prepares to make his return from injury.
Madrid coach Carlo Ancelotti has confirmed the Portugal captain is available for the trip to the Danish capital after a brief absence with a thigh problem.
Yet it remains to be seen whether the Italian trainer will opt to name a full-strength side, with away league games at Osasuna and Valencia coming hot on the heels of Tuesday's match.
Although Ronaldo has recovered from his injury, Ancelotti is still without the services of a number of first-team players.
Defenders Raphael Varane (knee) and Fabio Coentrao (thigh) are both sidelined together with midfielder Sami Khedira, who is expected to miss the majority of the season after damaging knee ligaments.
Sergio Ramos also misses out for Madrid, with the Spain defender suspended after being sent off in the 4-1 win over Galatasaray last month.
Should the Liga outfit score three or more goals, it will set a new record for the best goals return in the group stage.
Ancelotti's men have managed 18 so far, with Manchester United and Barcelona having previously scored 20.