The Old Trafford club are thought to be on the lookout for a new central defender as captain Nemanja Vidic is set to depart at the end of the season and doubts remain over the future of Rio Ferdinand.
Ginter has stood out in a Freiburg side that is mired in relegation trouble this season and his performances have reportedly caught the attention of United manager David Moyes, who is rumoured to be interested in a close-season deal.
Ginter himself has welcomed the links, although he insists there is nothing in the pipeline.
"If it is true, I am of course honoured and excited," he said in quotes reported by talkSPORT.
"On the other hand, there is still a long to the summer."
Germany manager Joachim Low has also recognised Ginter's displays for Freiburg by calling him up for the friendly encounter with Chile on Wednesday.
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