The 26-year-old enters the final 12 months of his contract with the Bavarians in the coming weeks, which has led to speculation surrounding his future at the Allianz Arena, with no agreement being made over an extension as things stand.
As a result, Arsenal have been linked with a move for their former player in recent days, and now SportBILD are suggesting that Bayern have set the Gunners a price tag of €40m (£34m).
However, current suggestions outline how a free transfer move upon the expiration of Gnabry's contract in June 2023 appears more likely at this stage, although Bayern have set the asking price anyway in case they are able to cash in on the Germany international in the upcoming transfer window.
Gnabry left the Emirates Stadium back in the summer of 2016 to make the move to Bundesliga outfit Werder Bremen for around £3.8m.
However, the winger was signed by Bayern for around £7m just 12 months later, before spending the 2017-18 campaign on loan at Hoffenheim.
Since joining up with the Bundesliga champions upon the completion of that loan spell ahead of the 2018-19 season, Gnabry has gone on to 63 goals in 171 appearances for the club across all competitions, helping them to lift 12 trophies during his stay so far.