Recent results have seen Hannover slip towards the relegation places and defeat in Sunday's local derby would leave them in the thick of the danger zone with five games of the season to go.
Korkut, who was appointed to replace Mirko Slomka in January, has been given the backing of club president Martin Kind, even though Kind recognises the situation is far from ideal.
"It's serious, really serious," Kind told the Bild newspaper. "But I'm convinced by Tayfun Korkut and am 120 percent behind him.
"He has my utmost faith. He's stable and he's doing a good job.
"Talking about his future is completely pointless. I can't and will not get involved in any such talk."
The situation is even more serious for Braunschweig coach Torsten Lieberknecht, but his future has never been in doubt in this, the club's first season back in the top flight.
He has also lifted the pressure on his side by suggesting they are not under as much pressure as Hannover.
"We're bottom of the table and Hannover are huge favourites," he said.
"We're looking forward to a highly emotional game while we want to use our strength at home to end the game with three points."
Three points could even lift Braunschweig off the foot of the table, although Lieberknecht is not concerning himself with that prospect
"It's out of our hands how the other teams play, which is why we're only focusing on our own game," he said.
"If we can overtake somebody on the last day of the season, then that would be a perfect time to do so, because nobody could catch us then."