With the Group B fixture at 3-0 to the Spaniards at the break, Balotelli thought it a good idea to swap playing shirts with Real defender Pepe when heading back down the tunnel.
Reds boss Brendan Rodgers only learnt about the shirt swap after the match and told Sky Sports that the controversial Italian will certainly have to explain himself.
"That's the first I've heard (about Balotelli swapping his shirt) and I wouldn't like it either," Rodgers said.
"It's something that doesn't happen here, it shouldn't happen here.
"We had a case of a player doing that last season which I dealt with and if that's the case again I'll deal with it again."
A 23rd-minute half-volley from Cristiano Ronaldo and a brace from Karim Benzema gave Los Blancos an unassailable lead at the break which was eventually enough to record a third win of the Champions League campaign.
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