The Daily Mail says acting on a tip-off from former Arsenal keeper Jens Lehmann, Gunners boss Arsene Wenger sounded out Borussia counterpart Lucien Favre to register his interest in the up-and-coming 22-year old, whose recent form has taken him into the senior Germany squad.
But though Favre is a personal friend of the Arsenal manager, he was in no mood to do him any favours.
Gladbach's Swiss coach said: "Yes, it’s true that Jens gave Arsene the information about Marco and I then received a call about him.
"I know Arsene very well, and I told him the truth about Marco, that he is a very good player and very interesting prospect.
"But I am the coach of this club, and my priority is doing the best for Borussia, rather than helping out an old mate.
"I want to keep Marco, and I think he will stay. How good is he? If I was in Arsene’s position and had to choose between Reus and Gotze, I don’t think I could. I would do my best to sign both.
"But I am confident Marco can resist the temptation of Arsenal. It might just be a little too early for him to move. It would be good for him, and for us, if he stayed another year or two. He has incredible qualities, but he can still improve in some ways, and we are working with him every day.
"He needs a foundation to keep improving his game, and he has the perfect one here at this club."