The Brazilian has enjoyed a solid first season in the Premier League after arriving from Corinthians.
The stopper, who has played 31 times in all competitions, may be on the move.
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Murillo is certain to leave if Forest are relegated, but may move even if they remain a top flight club.
Spanish news outlet Mundo Deportivo states that Real Madrid and Barcelona are chasing his signature.
Murillo will not have to think too hard about joining either of those Spanish giants.