The Sunday People reports that the Gunners watched the 19-year-old winger play for Schalke in a Europa League tie against Sporting Prague.
The teenager scored his seventh goal in nine games for club and country in the draw with Sparta Prague.
Sane recently signed a new five-year contract with the German side.
The Gunners are also reportedly continuing to keep an eye on AC Milan ace Stephan El Shaarawy.
The 22-year-old is currently on loan at Monaco from Italian side AC Milan.