Arsenal are an absolutely massive club, top managers want to manage the biggest clubs in the world. The size of the clubs fanbase, the clubs history and stature is a lot more important to most managers than the players he is working with. At the end of the season, he would no doubt leave little Mönchengladbach for Arsenal without hesitating, in the same way he would leave for another giant underperforming in the table like Milan, Bayern or United. The players he is currently working with are not that great either, he would work with a much better squad at Arsenal. Wherever Rose goes, he has the ability to work miracles, so the players are probably not the most important part.
Arsenal would also pay a lot more than Mönchengladbach where he has a small wage. The most likely destination is definitely Bayern after the season though.