The Danish outfit have never defeated Spanish opponents in eight attempts, but they will be buoyed by the 1-1 home draw earned against Juventus on matchday one.
Real were in imperious form in their opening group B fixture, Cristiano Ronaldo scoring a hat-trick in a 6-1 demolition of Galatasaray in Turkey.
The two sides have never met before, with Real's last game against a Danish side ending in a surprise 2-0 home reverse to Odense in what was then the UEFA Cup in 1994-95.
The last time Copenhagen came up against a side from La Liga was three years ago when they took a point from two games against Barcelona in the Champions League group stages.
That season they went on to deliver the best performance by a Danish side in the competition, reaching the second round before being eliminated by Chelsea.
Madrid exited at the semi-final stage of this competition for the third year in succession last season, while Copenhagen were edged out 2-1 on aggregate by Lille in the final qualifying round.
Carlo Ancelotti's side suffered their first league defeat of the season on Saturday, going down 1-0 at home to neighbours Atletico Madrid, a result that leaves them five points adrift of both Atletico and Barcelona at the top of the table.
World-record signing Gareth Bale is in line to feature, the Wales international coming off the bench during the weekend defeat after recovering from a thigh injury, but midfielder Xabi Alonso remains sidelined with a broken foot.
Copenhagen have suffered a terrible start to their domestic campaign and with just two wins from the opening 10 matches, Stale Solbakken's side currently find themselves in the relegation zone, their plight not helped by Saturday’s 3-2 defeat away at Brondby.
That reverse was Solbakken's first defeat since taking over from Ariel Jacobs in August and Copenhagen will be hoping to celebrate their 150th European game with what would be a surprise win.
