The Portugal international tried to confront the official in the tunnel after the game at El Madrigal and shouted at him: "What a robbery, you son of a b**ch!"
Romero is said to have mentioned Pepe's outburst in his report, meaning the incident is now likely to be reviewed by the Spanish Football Federation (RFEF).
The Portugal international was not shown a red card in the tunnel, as reported by other media outlets, but he could now face a lengthy ban of up to 12 matches.
Madrid coach Jose Mourinho could also be sanctioned for refusing to speak to the press after the game, following his dismissal for protesting the award of the free kick from which Marcos Senna cancelled out Cristiano Ronaldo's opener.
Madrid's fitness coach Rui Faria had earlier been sent to the stands, while defender Sergio Ramos and attacking midfielder Mesut Ozil both saw red after Senna's equaliser.
The draw at El Madrigal means that Madrid's lead at the top of La Liga has been reduced from 10 points to six points over the past five days.
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