The winger was tipped to potentially leave Eintracht Frankfurt during the summer transfer window, but ended up staying put at the Bundesliga club.
His future is again under the scanner amid interest from Newcastle, who are expected to invest heavily in their squad when the next transfer window opens.
However, according to German broadcaster Sport1, a move to Newcastle is not something Eintracht Frankfurt are concerned about.
For the Bundesliga side, losing Kostic is something which is not in their radar heading into the January window.
Eintracht Frankfurt are expecting that the 28-year-old will see out the season in Germany.
Kostic joined Eintracht Frankfurt in 2018 from Hamburg and has been playing his football in Germany since signing for Stuttgart in 2014.
A lucrative move to Newcastle could appeal to the Serbia international, but Eintracht Frankfurt are firmly opposed to letting him go in the mid-season transfer window.