The Daily Mail says Gotze will cost the Gunners £30million if they are to pry him away in January.
The 19-year-old scored the winner at Bayern Munich on Saturday and continues to attract attention all over the continent.
Arsene Wenger, though, insisted: "We have a big squad and we are not after anybody. Gotze is a very good player. I can understand there is a lot of interest in him around Europe.
"On our side, I do not think this is the best time to talk about it. We play against Dortmund tomorrow and we must concentrate on the game, not transfers."
Arsenal sent two scouts to watch Goetze against Bayern Munich, and chief executive Ivan Gazidis, together with key negotiator Richard Law, will discuss the club’s interest in Goetze with Dortmund officials this week.