The 25-year-old defender vented his frustration for his red card in Saturday's 3-1 victory against Sporting Gijon and went as far as to claim that his sending off had been 'premeditated' by the referee.
"Pique's comments are unfortunate and very serious," Arminio told Radio Nacional. "They make your blood boil, sportsmen must respect each other.
"His comments affect the state of refereeing and we will obviously report him."
In recent seasons, Real Madrid coach Jose Mourinho and his Barcelona counterpart, Pep Guardiola, were each fined €1,500 after the Refereeing Technical Committee complained about derogatory remarks from the duo over the standard of refereeing in the country.
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