The 26-year-old has excelled for the Foals this season, helping Marco Rose's side qualify for the Champions League.
The centre-back is reportedly a target for Chelsea boss Frank Lampard, who is looking to bolster his defensive options after conceding 54 goals in the Premier League.
But despite interest from the Blues - as well as Inter Milan and Atletico Madrid - Ginter insists he is not looking to leave the Bundesliga outfit.
“I’m definitely staying in Gladbach,” Ginter told German outlet Kicker.
“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 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.”