The Germany centre-back has been linked with the likes of Chelsea, Inter and Atletico Madrid.
However, after a 2019-2020 season that saw Gladbach finish fourth in the Bundesliga and qualify for the Champions League, Ginter wants to help the Foals take the next step.
"I'm definitely staying in Gladbach," Ginter said.
"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."