The Red Devils are known to be on the lookout for a centre-back with Nemanja Vidic set to leave the club at the end do the season and Rio Ferdinand’s future also in doubt.
David Moyes is believed to have made use of a weekend off of Premier League action to travel to Germany to watch the 20-year-old in play against Hertha Berlin on Friday night.
Ginter is already thought of as one of the best emerging defenders in the Bundesliga, and has previously been linked with Arsenal.
With Champions League qualification for next season looking unlikely for the Old Trafford side, Moyes is rumoured to be looking at some more realistic targets.
Ginter is seen as just that, with the youngster unlikely to demand top-level continental football at an early stage of his career.
The starlet is valued at around £10m, which would barely make a dent on United’s rumoured £200m transfer budget.
The Premier League champions are not in action this weekend due to the Capital One Cup final altering a number of scheduled games.