According to a report from English broadsheet The Daily Mail, the Gunners are primed to use Tuesday's Champions League encounter with Dortmund as an opportunity to register their interest in the precocious 19-year-old playmaker.
In fact, the Gunners dispatched two of their scouts to Germany over the weekend and promptly caught Gotze netting the winner for his side against Bayern Munich in the Bundesliga.
Arsenal chief executive Ivan Gazidis, along with negotiator Richard Law, will begin informal discussions with Dortmund officials when the German side make the trip to London for their European excursion.
However, any hopes of landing the youngster on the cheap will be met with short shrift by Dortmund, with the club making it clear that only an offer in the region of £30m will allow the Gunners to buy one of Europe's most hottest properties.
Any potential deal would easily double the record fee the Gunners forked out when they paid £15m to Zenit St Petersburg for current midfielder Andrey Arshavin in 2009.
Although Dortmund will fight tooth and nail to keep Gotze at least until the end of the current campaign, they have realized that the vultures of elite European outfits circling around their starlet will make it impossible to retain his services over the next few seasons.
Any concrete offer of £30m would have to be seriously considered by the club should any offer arrive in the forthcoming January transfer window.
However, Dortmund will shield Gotze from any potential distractions ahead of their must-win clash against the Gunners at the Emirates.
Gunners chief Arsene Wenger is looking to supplement his squad with creative talents following the crushing departures of stalwarts Cesc Fabregas and Samir Nasri.
Wenger, who has a reported £50m war chest, is willing to spend a large chunk of his transfer kitty on Gotze.