The former Norwich City man would cost a reported £35 million pounds, per The Sun.
It would make Tzolis the most expensive Greek Premier League signing of all time.
The exciting winger had a stellar season in Belgium's top flight, netting 17 times and providing 23 assists in 36 games.
Mikel Arteta's champions are looking to strengthen their squad after Leandro Trossard departed the club for Beskitas in a £17.1 million deal.
Arsenal also remain in the hunt for Aston Villa's Morgan Rogers, and it is believed any potential move for the Englishman would not impact the signing of Tzolis.
The Gunners have already made two signings so far this window, the permanent signing of Piero Hincapie from Bayer Leverkusen and goalkeeper Illan Meslier from Leeds, and Tzolis could soon be added to the list of summer arrivals.