The midfielder is one of the hottest properties in Europe and is wanted by a host of top teams.
A new report from transfer expert Fabrizio Romano states that both Arsenal and Bayern Munich want to sign Zubimendi.
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He tweeted: "Understand Martin Zubimendi remains on Arsenal list. And he was on top of Bayern list in case Xabi Alonso was gonna become their new coach.
"Bayern still appreciates Zubimendi as one of the targets but final decision will be up to next manager. It's all quiet with Barca."
When asked about his future recently, Zubimendi said: "I have never planned to leave Real Sociedad, I always say that. I love life here, at home, I'm so happy here.
"The values of this club are the same as mine so I feel very good, I always said that I'm happy."