The France defensive midfielder, 29, has a £30million release clause with the Spanish outfit. But new Gunners boss Unai Emery is aware that any further signings will have to be on the cheap after a busy window.
The Gunners have picked up five players so far this summer, splashing out close to £70m.
Nzonzi, 29, was a regular during Emery’s two seasons as Sevilla boss.
He has been a long-time target for the Gunners, who want to bolster their defensive set-up before their opener against Manchester City on August 12.