Arsenal are on the hunt for a new goalkeeper to provide some competition to Premier League stalwart Petr Cech.
Leno has one year left on his contract at Leverkusen and German outlet SportBild claim they could allow the shot-stopper to leave for as little as €20million (£17.6m).
The 26-year-old missed out on a spot in Germany’s World Cup squad meaning any deal with Arsenal could be easier to complete quickly.
Leverkusen sporting director Rudi Voller recently told Bild: “Leno can leave but only on our terms.
“We are still in constant and open exchange with Bernd and his manager.
“Leno already had a concrete offer from Napoli in 2017, but we didn’t have an equivalent backup at the time.
“He had to stay and he did really well last season, but we thought Bernd’s desire to leave would resurface and so with the arrival of Lukas Hradecky, we have a high quality successor.”
Leno kept 12 clean sheets for Leverkusen in all competitions last season.
After playing 33 appearances in the Bundesliga in 2017/18, he kept 10 clean sheets, conceding 40 goals throughout the domestic season.
He amassed a save percentage of 64 per cent during the campaign.