The North London outfit are believed to be hunting a long-term replacement for Petr Cech, whose contract expires at the end of next season.
According to Bild, Leno is on Arsenal's radar, but they could face competition from Serie A side Napoli, who are also keeping an eye on the 26-year-old shot-stopper.
The German publication claims that the Leverkusen keeper, who has only missed three games in the past seven years for the Bundesliga outfit, has a £22m release clause.
Arsenal are also reportedly in the market for a central defender and holding midfielder this summer, but doubts remain over Arsene Wenger's position as manager.
Reports have emerged claiming that the Frenchman needs to guide the Gunners to Europa League glory in order to keep his job at the Emirates.