Olise is contracted to Bayern Munich until 2029, but Rummenigge expects the club to begin discussions over a new agreement at some stage.
“Olise has a contract until 2029. At some point you will have to talk to him and make him an appropriate offer,” Rummenigge told Abendzeitung.
The former Bayern chief executive rates Olise among the outstanding players in his position and believes only Barcelona's Lamine Yamal currently belongs in the same conversation.
“Olise is outstanding in his position. There are two top players there: him and Lamine Yamal. Olise's game is even more mature at the moment,” he said.
Olise was linked with Real Madrid during the summer, while Bayern chief executive Jan-Christian Dreesen recently admitted it remains uncertain whether the club can keep the France international permanently.
Rummenigge also criticised the attention surrounding some of Olise's interviews, arguing that the winger's performances on the pitch should remain the priority.
“I much prefer someone to give their best in their actual job – in this case on the pitch – than in interviews,” he said.
Rummenigge also addressed his decision over Eberl's contract extension, admitting he initially intended to vote against it before ultimately abstaining.
“I thought for a long time about whether I should vote 'no' on Max's extension. It was only during the meeting that I decided to abstain. I stand by that,” he said.
Eberl nevertheless secured enough support to extend his Bayern contract until 2029.
Rummenigge said it was important that he made his decision independently rather than being influenced by a recommendation made beforehand.