Leverkusen take on improving Werder Bremen on Friday less than a week after their 6-2 Bundesliga demolition by Borussia Dortmund triggered the departure of coach Roger Schmidt.
Former Turkey international Korkut, who signed up until the end of the season, is now tasked with helping them secure a Europa League spot for next season.
Currently in 10th place on 30 points after losing four of their last six league games, Leverkusen are 13 points away from third place that leads to the Champions League group stage and three behind the last Europa League qualification place.
They also face Atletico Madrid in their Champions League round of 16 second leg next week having lost 4-2 in Germany last month.
"We want to do everything possible to reach our goal of playing international football next season," Korkut told reporters this week. "In the remaining games, we will try to lead Leverkusen to the international spots where the club belongs."
Schmidt had managed to qualify Leverkusen to the Champions League for three consecutive seasons.
Korkut will not have to worry about a lack of quality in his squad with an array of internationals including Germany's Karim Bellarabi, Kevin Volland and Jonathan Tah, Mexican striker Javier Hernandez and Chile's Charles Aranguiz.
But what he will need to worry about is the inconsistency that has peppered his team's games this season.
"Turning everything around at this stage of the season makes little sense," he said. "But our style of play should be a bit more controlled here and there than recently. But to plant something new, there is just no time."
They are also without playmaker Hakan Calhanoglu, suspended until the end of the season over a contract dispute, in the most crucial part of their campaign.
Former Bundesliga champions Werder, battling to avoid relegation, are in fine form, having won their last three matches to climb out of the bottom spots and into 14th place.
Led by hugely talented Germany international Serge Gnabry, who is his team's top scorer with 10 goals, coach Alexander Nouri has every right to eye a contract extension if they avoid the drop.
He will, however, be without captain Clemens Fritz, who will require surgery for an ankle ligament injury and was ruled out this week for the remainder of the season.
Leaders Bayern Munich, seven points clear at the top, host Eintracht Frankfurt while second-placed RB Leipzig entertain VfL Wolfsburg.
(Reporting by Karolos Grohmann; Editing by Alison Williams)
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