Gnabry initially joined Arsenal from Stuttgart in 2011 but failed to become a first-team regular for the club, only making 18 appearances in all competitions before leaving for Werder Bremen.
Bayern then signed the Germany international in 2017, and he has since made 171 appearances for the Bundesliga champions, scoring 64 goals and contributing 40 assists in the process.
The 26-year-old's future is currently the subject of much speculation, though, with his current deal at Allianz Arena due to expire in June 2023.
According to Bild, Bayern have offered the attacker the chance to double his salary to a figure in the region of £14m, but the attacker has reservations over signing an extension, as he is unsure whether he will be a key player for the club moving forward.
The proposed agreement would place the Germany international alongside Kingsley Coman and Leroy Sane in terms of the highest earners at Allianz Arena, but he is not believed to view the wage packet as a priority.
In all competitions, he featured on 45 occasions this term, contributing 17 goals and 10 assists in the process, including 14 goals and six assists in 34 Bundesliga matches.
According to German journalist Christian Falk, Arsenal are also keen to sign the forward, but their failure to qualify for next season's Champions League makes a deal unrealistic this summer.
Falk claims that Mikel Arteta's side could instead attempt to bring him back to North London on a free transfer next summer, but that would rely on the player deciding to run down his contract.
Arteta's side had been in pole position to secure fourth spot in the Premier League table heading into their final three matches of the campaign, but back-to-back losses to Tottenham and Newcastle United handed the advantage to Spurs, who secured the final Champions League spot on the final day.
The Gunners will be back in Europe next term, though, with fifth spot in the table seeing them qualify for the group stage of the Europa League alongside Manchester United. body check tags ::