Chelsea have also been linked to the 22-year-old by the Daily Star.
The Express has also mentioned that Wolfsburg are in pole position to sign the defender, who is apparently rated at £18 million. With so many top sides interested in the youngster it is unlikely that his future will be resolved soon.
The Red Devils and their local rivals are both in dire need of a new centre-back, for differing reasons. Rudiger could be the man to help them, having helped VfB to avoid relegation in 20 appearances for them last season. The player did well enough to earn a competitive debut for his country last October.
United had to rely heavily on David De Gea last season, with Phil Jones, Chris Smalling, and Jonny Evans all looking error-prone at times. As such a reliable man at the back will be a necessity for their foray in to the Champions League next time round. Especially if the goalkeeper makes a move to Real Madrid, which the Daily Telegraph has rumoured will happen.
Meanwhile, the Citizens need someone to partner captain Vincent Kompany at the heart of their defence. Although the Belgian made mistakes at vital moments in the last campaign, he is still of a higher quality than Eliaquim Mangala and Martin Demichelis. Having a reliable player alongside him may even help the 29-year-old get back to his best.