The Brazilian has been a revelation in the Premier League since signing from Corinthians.
While he only arrived in August, he is ready to move on if Forest are relegated.
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Per Mundo Deportivo, he will be sought after by several top clubs, including Manchester United and Real Madrid.
While Los Blancos would be a more appealing destination, Murillo may have to think about game time.
He is much likelier to become a regular starter at United, given their defensive issues.