Centre-back Ginter turns 28 next month and his contract is due to expire in June 2022.
He announced via social media yesterday that he would not be extending his deal, so will be a free agent at the end of the season.
Inter have long been chasing the defender, but Spanish newspaper Diario AS point out there is also interest from Bayern Munich and Barcelona.
Meanwhile, today Borussia Monchengladbach also confirmed that Zakaria will not be signing a new contract, so he too will be free to move from the summer.
Roma and Juventus have been heavily linked with Switzerland international midfielder Zakaria, who joined Gladbach from Young Boys in 2017 for €12m.
So far this season, he has scored two goals in 16 competitive games for the German club.
Official. Denis Zakaria has communicated to Borussia Mönchengladbach his plan to leave the club as free agent at the end of the season. 📩⚪️ #BMG
FC Bayern, Barcelona, Juventus and two English clubs are in contact with his agent. Nothing agreed/decided yet.
— Fabrizio Romano (@FabrizioRomano) December 29, 2021