The 26-year-old German, who has been at Leverkusen since 2011, is yet to have a medical with the Premier League club.
Petr Cech and David Ospina are the Gunners' frontline goalkeepers, and it is unclear who would make way for Leno.
Arsenal are also optimistic about reaching a deal to sign 22-year-old Sampdoria midfielder Lucas Torreira, who is at the World Cup with Uruguay.
New Gunners boss Unai Emery has already signed defender Stephan Lichtsteiner from Italian champions Juventus on a free transfer.
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