The interest has been reported by Radio Nacional de España journalist Silvia Barba, who says Atletico are considering the former Real Sociedad midfielder as a potential addition to Diego Simeone's squad.
Atletico Madrid invested heavily during the summer, but sporting director Mateu Alemany is understood to believe there is still room to improve the squad. Zubimendi's ability to dictate possession, organise play and provide defensive protection makes him an attractive profile for the Spanish club.
Zubimendi joined Arsenal from Real Sociedad in the summer after establishing himself as one of LaLiga's leading holding midfielders. Real Madrid had also previously monitored him.
A move would not be straightforward, however. Zubimendi is an established international and Arsenal would have little reason to part with an important player unless the circumstances and financial terms suited them. The midfielder's reported reduction in minutes could become a factor, but there is no confirmed agreement or negotiation between the clubs.
Simeone would value the possibility of pairing Zubimendi with Pablo Barrios in central midfield. The Atletico coach is looking for balance and control in that area, and the Arsenal player's passing range and positional discipline could complement Barrios' qualities.
The report has also prompted speculation about Julián Álvarez, whose form and relationship with sections of the Atletico support have come under discussion following his performance against Barcelona.
The Argentina forward was linked with Arsenal during the previous summer window, although the London club did not make a decisive move to sign him.
That has led to suggestions that Álvarez and Zubimendi could become connected in a potential transfer arrangement. However, RNE's report does not establish that the clubs are negotiating a swap, and such a scenario remains speculative.
For Atletico, Zubimendi would represent a significant addition to a midfield that Simeone wants to strengthen. The prospect of regular football at the Metropolitano could appeal if the midfielder's role at Arsenal does not develop as hoped.
No deal is imminent. Any move would depend on Arsenal's willingness to negotiate and whether Atletico can present an acceptable offer.