Ginter has been linked with the likes of Chelsea, Atletico Madrid and Inter Milan after impressing at the back for Marco Rose’s men in the just ended Bundesliga campaign.
The 26-year-old Germany international was part of a Monchengladbach defence that finished fourth last season and conceded just 40 goals, the third least in the German top flight.
Ginter has acknowledged interest in his services but is not interested in moving away just yet.
"I'm definitely staying in Gladbach," Ginter told Kicker magazine.
"Of course I heard of the enquiries and was flattered by this attention, but I've said often enough how good things are for me in Gladbach.
"This team has huge potential. And the coach [Marco Rose] gives us a great deal of added value.
"With the amazing fans and surroundings here, this club is currently in the process of building something. I share these big ambitions and I also have a contract here."
Ginter joined Monchengladbach from Borussia Dortmund in the summer of 2017.
He has won 29 caps for the German national team and was part of their squads at the 2014 and 2018 FIFA World Cups, but failed to make a single appearance at either tournament.