The midfielder will leave Athletic Bilbao after 15 years and he could make the move to Argentina and River.
At his farewell presentation, Muniain said: "I am closing a circle in a good moment.
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"We have been through many things together, inside and outside the locker room. We have experienced wonderful things and others not so much and we have faced them as best we could.
"I hope I have been able to help you grow a little and understand the Athletic feeling a little more and what this shirt entails in terms of attitude, commitment, knowing how to lose, respecting your rival and your teammate.
"You are capable of continuing to do so with those who come."