According to Sky Sports News, Louis van Gaal is lining up a move for Rudiger should they fail to land Sporting Lisbon's Marcos Rojo.
It looked like United could seal a deal for the Argentinian star when he requested a transfer and went on strike earlier this week. However issues with the player's ownership have seemed to put the brakes on any potential move.
Rojo has also apologised tonight for his actions earlier this week, which suggests he could remain in Portugal for the foreseeable future.
Not much is known about Antonio Rudiger and his link to United is a brand new rumour. He has previously been linked with Monaco, Chelsea and West Ham United, who reportedly had a bid rejected earlier this summer.
Here are five facts for United fans need to know about the youngster:
1) He is only 21-years-old, which is extremely young for a defender. He won't be that experienced leader that United are crying out for in defence but he does posses great potential.
2) Rudiger is of German nationality and has represented his country at every single youth, and at senior level. He made his debut for the World Cup winners on 13 May 2014 in an international friendly against Poland. The Stuttgart man helped them to keep a clean sheet in the 0-0 draw.
3) He plays as a central defender for VfB Stuttgart. Despite his age, Stuttgart are Rudiger's sixth club, and before them he played for their Bundesliga rivals Borussia Dortmund.
4) Despite Stuttgart finishing 15th, the German was a key figure in their Bundesliga campaign last season making 30 league appearances and scoring 2 goals.
5) Antonio Rudiger's contract doesn't expire until 2017, but he hasn't completely ruled out a move to England. He told Sport-BILD: "It's fine to find out other clubs are interested in me. But my full focus is on Stuttgart.
"I am under contract until June 2017 with the club and I do not force a move at this point in time. Of course, you never know in football. Still I am just focused on my job and the new season."
Do you think Antonio Rudiger would be a good signing for United?