Former Hannover and Kaiserslautern boss Korkut took over the reins at the BayArena in March, after Roger Schmidt's dismissal.
However, the 43-year-old has been unable to salvage Leverkusen's dismal campaign, taking just eight points from his 10 games in charge - claiming just one win.
And, after Leverkusen's 2-2 Rhine-derby draw with Cologne, Schade was blunt on the coach's future.
"He has helped us in a difficult situation, but football is a sport of course, and we can not be satisfied," said Schade.
Leverkusen - who sit in 12th place on 38 points - face Hertha Berlin in their final Bundesliga game of the season.