The 32-year-old will be out of contract at the end of the season, but City are expected to offer him a new deal.
Gundogan is also a target for Barcelona and is attracted to the idea of joining the Spanish champions.
He has not made a final decision on his future yet and Arsenal have now expressed an interest in bringing him to Emirates Stadium.
Arsenal manager Mikel Arteta worked with Gundogan during his time as an assistant at City and remains a fan of him.
Arteta’s side have faded towards the end of the title race this year, with City crowned champions on Sunday, and Arsenal plan to bolster their squad this summer.
Gundogan would bring a wealth of experience having won five League titles during his time at the Etihad.
The German has played a leading role for City this season and has been in top form lately, scoring four goals in his last two League games.