Sport says Zubimendi could move to the Emirates during the summer transfer window.
The midfielder is betting on the Gunners to activate his £52.9million release clause.
Barcelona have also registered an interest in the Spain international but the North Londoners are leading the way.
Journalist Eugenio Mateo Serrano told Calciomercato after being asked about Zubimendi moving to Barca: "I do not think so. Xavi needs another player instead of [Sergio] Busquets.