The 22-year-old has scored nine goals in 12 appearances across all competitions this season, including four in his first two Champions League matches, according to The Sun.
Mikel Arteta is assessing his attacking options after Kai Havertz started all seven of Arsenal's Premier League fixtures so far, while Viktor Gyökeres has not been a regular league starter. Gyökeres has featured from the beginning in both of Arsenal's Champions League games but has yet to score in the competition.
Tresoldi's recent performances have strengthened his case as a potential addition. He scored in Club Brugge's 3-2 defeat against Aston Villa before producing a hat-trick in a dramatic 4-3 Champions League victory over Inter Milan at San Siro.
Arsenal are reported to be exploring the possibility of a January move, although no formal offer has been confirmed.
The Gunners have a recent relationship with Brugge after signing Christos Tzolis in the summer. That connection could help discussions, particularly as Tresoldi and Tzolis were among the Belgian Pro League's leading scorers last season.
Tresoldi finished the league campaign with 19 goals in 40 appearances, while Tzolis ended just two goals behind him. Arsenal could see the prospect of reuniting the pair in north London as an attractive way to strengthen their forward line.
However, the financial demands could prove significant. Brugge reportedly rejected a £30 million offer from Roma in August, and Tresoldi's valuation is now said to have risen to around £42 million.
Arsenal would also face competition from Italy. AC Milan are reported to be keen on the striker, who is a childhood supporter of the club, potentially giving them an advantage if they decide to pursue a deal. Inter Milan have also been linked with interest.
Tresoldi, who represents Germany at Under-21 level, has options to consider at international level because of his family background, but his immediate focus is on maintaining his scoring form for Brugge.
Arsenal's reported interest reflects the search for additional firepower, but any move will depend on Brugge's willingness to negotiate and the level of competition for the striker's signature when the winter window opens.