Moyes took in Freiburg's goalless draw with Hertha Berlin last week, with Ginter understood to be the reason for his presence at the Olympic Stadium.
Ginter is rated as one of the best young defenders in the Bundesliga and has been called up to the full Germany squad for their clash with Chile on Wednesday when he is expected to make his debut.
The 20-year-old's form has also seen domestic giants Bayern Munich and Borussia Dortmund show an interest, and this has led to speculation that he could be set for a summer switch.
The player will not talk about his future but admits a big move is something very much on his radar, although he concedes that does not mean it will be Bayern.
"I am unable to publicly discuss negotiations, this should remain behind closed doors," the centre-half told SPORT1.
"It's definitely good to know great clubs are interested in my services. It's an honour to see clubs like this being keen.
"It's my goal to play for a big club one day in the future. This is no secret.
"It doesn't need to be Bayern Munich. Still, to play for a big club is the dream of every football player."