The Serbian fullback is a target for David Moyes this summerwith the London club willing to meet Frankfurt’s asking price of around £12.75 million.
Still, there were doubts that the 29-year-old would be willing to trade Champions League football with the Bundesliga for the Europa Conference League at West Ham.
With just a year left on his contract with Frankfurt, there is also the possibility that Kostic could make a more lucrative transfer as a free agent next summer.
The signing of a new left-back to cover and compete with Aaron Cresswell has been a priority for Moyes, although the club seems to have to look elsewhere on that front.
Speaking to Sky Germany, Glasner said: “I don’t know what will happen until September 1, but from today I’m sure he will stay.”