The defender arrived at the start of the season from Corinthians and signed a five-year contract.
Having played 31 games this term, Murillo has impressed in the Premier League.
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Per Mundo Deportivo, both Real Madrid and Barcelona are eyeing a summer transfer.
Manchester United, Chelsea, and Liverpool are also monitoring his progress.
Murillo must now decide if he wants to move to a top club this summer, or continue his development at Forest.
If the City Ground club avoid relegation, they may be able to convince him to stay for another year.