But according to John Edwards of the Daily Mail, it doesn't look as though Gotze will be heading to the Emirates any time soon. Or perhaps any time at all, for that matter:
In a departure from their normal cautious approach to spending, Arsenal are even prepared to meet the €37 million (£31.5 million) release clause in a recently-signed contact that runs until 2016.
But while Dortmund would be obliged to accept such a bid, it would appear Gotze might be less inclined to meet Wenger for talks, after his agent Volker Struth said: "Mario has not even thought about leaving Dortmund in 2013. He is totally not interested in that and will stay at least another season."
It gets worse for Arsenal. According to Edwards' report, Gotze had the following to say when asked if he would consider leaving the club:
"I am very happy at Dortmund and satisfied with the way we are progressing as a team," he said. "Any thoughts about playing for another team are very much for the future, but Real Madrid, Barcelona or Manchester United could be interesting."
Gotze would be perfect for Arsenal's system, and Wenger's rumored interest makes a ton of sense.
With his pace, vision, creativity, deft touch, ability to both facilitate on the attack and score goals himself, and with plenty of room to grow into an even better player—remember, he's just 20 years old—he would be the next great star at Arsenal.
Seriously, this kid is a wizard with the ball.
A future with Gotze and Wilshere in the midfield would be a whole lot of fun to watch. Add Cazorla into the mix next year, and you've got more maestros in the midfield than Wenger would know what to do with.
It's a shame it probably won't happen.
The saving grace for Arsenal is that, at least in the short term, the team has bigger needs than an attacking midfielder. For as solid as Mikel Arteta has been this year, adding a true, physical holding midfielder should be the team's top priority.
Plus, the team could use another striker. While Arsenal fans would love to see a player like Stevan Jovetic, even adding a player to support incumbent Olivier Giroud like Loic Remy would make sense.
And let's not forget about right-back—Bacary Sagna's days at the club are likely numbered—or keeper, where an upgrade is needed.
Still, Gotze would be so awesome in Arsenal's system, you can't help but dream and hope that he might someday come to the Emirates. It may be a long shot, but at least Wenger has his eyes on some of Europe's biggest prizes.
Or at least he supposedly does. Like every other Arsenal supporter, I'll believe it when I see it.