Reports in Germany last month revealed David Moyes had been to watch the 20-year-old in action, and is considering a summer bid for his services.
Ginter is considered one of the most exciting prospects in Germany, and has previously been linked with a switch to both Bayern Munich and Arsenal.
David Moyes is desperately seeking defensive reinforcements for the summer, with Nemanja Vidic already confirming his departure, and Rio Ferdinand likely to follow.
Ginter hinted he would be interested in a move to the reigning Premier League champions, but also admitted there was a long way to go between now and the end of the season.
“If it is true, I am of course honoured and excited,” Ginter said.
“On the other hand, there is still a long way to the summer.”
Ginter has a contract with the struggling Bundesliga side until the summer of 2017, and would likely cost in the region of £10million.