The 24-year-old Greece international scored 22 goals and provided 29 assists across 52 matches for the Belgian side this season, numbers that have caught the attention of several Premier League clubs.
According to BBC Sport, Arsenal sporting director Andrea Berta is actively working on a deal for the winger, with manager Mikel Arteta said to be on board with the move.
Tzolis joined Club Brugge from Fortuna Dusseldorf in the summer of 2024 for around €6.5 million, a deal that now looks like one of the shrewdest pieces of business in recent Belgian football history.
Reports suggest Arsenal have been in direct contact with Brugge over the winger, with the fee likely to be the key sticking point in any negotiation.
Speaking in a video posted on social media, Tzolis addressed the speculation directly.
"I hope that Arsenal will come knocking," Tzolis said.
"If Arsenal come, it would be a privilege for any player to get to play for them."
Brugge are reportedly seeking a fee in the region of €40 million, which would set a new Belgian transfer record.
The current record stands at €37.5 million, and Brugge are under no financial pressure to accept anything less given Tzolis is under contract until the summer of 2029.
Arsenal are not believed to be alone in their interest. Manchester United and Chelsea have also been credited with tracking the Greek international, whose combined output over the past two seasons stands at more than 40 goals and 40 assists in all competitions.
Tzolis is no stranger to English football, having joined Norwich City as a teenager in 2021 before loan spells at FC Twente and Fortuna Dusseldorf helped rebuild his career.
He made his Premier League debut for Norwich against Arsenal at the Emirates Stadium, a detail that adds an extra layer to the current speculation.
Arsenal's interest in Tzolis comes as the club continues to reshape its attacking options following last season's Premier League title and Champions League final defeat to Paris Saint-Germain.
Reports indicate the move would not affect Arsenal's separate pursuit of Aston Villa's Morgan Rogers, with recruitment staff viewing Tzolis as a distinct opportunity rather than a like-for-like alternative.
On the international stage, Tzolis has nine goals in 34 caps for Greece, and his club form has only added to calls for a more prominent role with the national team.
For now, the ball is in Brugge's court. Arsenal have shown their hand, and Tzolis has made his feelings clear. What happens next depends on whether the two clubs can find common ground on a fee that both sides can accept.