The 32-year-old former Germany international joined Leverkusen 10 years ago from Nuremberg and has scored a total of 139 goals in 371 Bundesliga games for the two clubs.
"Stefan Kiessling is both for us and our fans an identity figure and we really wanted to keep him," Schade said in a statement.
"That is why we agreed that he will work at the club after the end of his career as a professional player. We will see exactly in what capacity that will be."
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Leverkusen look set to qualify for next season's Champions League as they sit third in the Bundesliga with four games remaining.
(Reporting by Karolos Grohmann. Editing by Patrick Johnston)
