The Germany international is set to leave the Westfalenstadion this summer alongside manager Jurgen Klopp after a successful few years in the yellow shirt.
With Gundogan a Bundesliga champion and a Champions League Final goalscorer, interest in his signature is high, with Manchester United having been heavily linked with a move.
The Red Devils have widely been hailed as favourites to land him, but now reports claim that Arsenal are firmly in the running.
Arsene Wenger is set to delve into the transfer market in the coming months, with his Gunners side having booked an automatic route into the Champions League group stage via a third place finish in the Premier League.
Gundogan has endured an injury hit 18 months, in which he missed his nation’s glorious World Cup campaign.