Both teams have looked bare at the back this term when injuries have struck and are said to be in the market for a defender.
Both are also said to be after the same player, Borussia Dortmund star Mats Hummels.
Valued at £47 million by some, and £32 million by others, there is no doubt that he is an expensive acquisition, but he would be a worthwhile one.
Plus, Dortmund are struggling in the Bundesliga.
Ahead of today's game against Eintracht Frankfurt they sat rock-bottom of the Bundesliga. The club have been hounded by serious injuries to some of their key players and their recent additions have not exactly caught fire just yet.
With relegation a genuine possibility Arsenal and Manchester United will certainly be hoping they get the player.
However, he seems content to remain at the club, even if they get relegated.
He was asked if his contract at the club would remain valid should his beloved Dortmund drop into 2. Liga. His response:
"I don't know. I have no idea. Probably yes, but I really do not want to think about departing right now."
Dortmund probably won't be relegated from the Bundesliga this season anyway, despite the difficulties currently affecting the team.
But Bundesliga or Liga. 2, it will always be a tough task for United or Arsenal to pry Hummels out of Westfalia.