The Portugal international was seen to nudge into Messi when the World Player of the Year was on the floor after a tackle, then stood on his hand as he walked past around 20 minutes from the end of the game.
When asked about Pepe during the post match news conference, Real coach Mourinho first said he had not seen the incident.
A second reporter asked if Pepe's action would merit internal discipline from the club if he thought Pepe had stood on Messi's hand intentionally.
"Obviously if it is intentional, is it punishable," Mourinho replied.
Real's deployment of the robust centre back in a midfield destroyer role alongside Xabi Alonso and Lassana Diarra signaled their intentions in seeking to disrupt Barcelona's trademark link-up play and look for swift counter-attacks.
Pepe, sent off in the Champions League semi-finals against Barca last year, picked up a yellow card early in the first half after catching Sergio Busquets's foot with a late lunge.
Mourinho substituted Pepe before the end of the game to whistles from the Bernabeu crowd.
Although I don't like Barcelona , no doubt Bareclona is the best football team in the world . Confronting such a strong opponent , Real Madrid should do three hundred percent better than usual . But such a foul that violates sports spirit should be banned and Pepe must afford the cost for what he has done.