Born in Sestao, Biscay, Basque Country and raised in neighbouring Portugalete, Nuñez joined Athletic Bilbao's Lezama academy in 2007, aged ten.
[6] After making 36 appearances in 2017–18, Nuñez played far less (14 matches) during the 2018–19 season, initially finding himself behind rookie Peru Nolaskoain as well as Iñigo Martínez and Yeray Álvarez in the queue for selection in the position.
[14] He was called up to the full side by manager Robert Moreno on 30 August 2019, for two UEFA Euro 2020 qualifying matches against Romania and the Faroe Islands.
He has also played for the unofficial Basque Country team, making his debut against Costa Rica in November 2020 and scoring the winning goal with a header in the closing minutes.
[17] Nuñez's father, Abel, was also a footballer and a defender who mainly represented Barakaldo CF during his career,[18][19] having migrated from Galicia to the Basque region when young.