According to The Sun, the two clubs are nearing a resolution on the fee, which would make the 24-year-old the most expensive departure in Club Brugge's history, surpassing the €37.5million Charles De Ketelaere transfer to AC Milan in 2022.
Tzolis joined Brugge from Fortuna Dusseldorf in 2024 for around €6.5million and has gone on to score 43 goals and provide 45 assists in 108 appearances for the reigning Belgian champions.
The Greece international, who won 34 caps for his country, would replace Leandro Trossard in Mikel Arteta's squad, with the Belgian winger closing in on a move to Besiktas. Standing 1.79m tall and predominantly a left-footed player operating on the right, Tzolis is seen by Arsenal as the ideal like-for-like option to fill the void left by Trossard's departure.
Arsenal are also working to finalise a separate deal for Newcastle United midfielder Bruno Guimaraes as they continue an active summer of recruitment following last season's Premier League and Champions League final exploits under Arteta.
Tzolis previously spent time in English football with Norwich City, managing only a handful of appearances before returning to the continent, but has since rebuilt his reputation in Belgium, where his form last season made him one of the most productive wide players in Europe. Sporting director Andrea Berta has been driving the push to bring him to north London, with Arteta said to have already given his approval for the move.
Should the transfer go through, Tzolis would arrive at the Emirates Stadium as the most expensive Greek player in history, surpassing the fee Brighton paid for Babis Kostoulas, and underlining the scale of Arsenal's ambitions as they look to strengthen an already title-winning squad for the season ahead.
The move would not affect Arsenal's continued interest in Aston Villa forward Morgan Rogers, who remains a separate target regardless of how the Tzolis deal develops.