Mallorca "are always against any type of racism", the Balearic club said in a statement released on Monday in response to the shouts with xenophoic connotations which Real Madrid player Vinicius Junior received at Son Moix.
The Mallorcan side are "working together with La Liga to identify the culprit of Sunday's racist abuse to then take appropriate legal action", they added.
The club also "want to thank, with this case put to one side, the exemplary behaviour of our fans in the game against Real Madrid", the announcement read.
Vinicius was whistled by the home fans each time he ran down the wing while being chased by full-back Pablo Maffeo and centre-back Antonio Raillo, who he had several head-to-head battles with throughout the game's 98 minutes.
The three players had already gone up against each other before, being at the centre of great tension on the pitch and in the stands.
The Brazilian was being taunted and jibed when he was going to the Madrid team bus when leaving the stadium.