The France international had reportedly hoped to move to Real Madrid over the summer, a preference first reported by FT in mid-July, with further reports suggesting the 24-year-old is eager to test himself elsewhere before too long as he continues to develop as a player.
Dreesen used his appearance on Sport1's Doppelpass on Sunday morning to swat away the various rumours that circulated over the transfer window, stating firmly that "we had no offer on the table" from Madrid or any other club.
Despite that dismissal, the Bayern chief executive stopped short of promising Olise would remain at the club beyond this season when pressed on the matter.
"Making promises in this business is a difficult thing to do. Whether we can keep hold of him permanently is something we'll discuss again next summer," Dreesen said, when asked directly whether Olise would stay past the current campaign.
The winger's contract runs until 2029, and Dreesen was unequivocal about his importance to the team in the meantime.
"Olise is incredibly important for this side. He's a magician on the pitch," he said. Reports in recent weeks have nonetheless suggested that extending the left-footed playmaker's deal is not currently high on Bayern's list of priorities, potentially reflecting the complexity of negotiations that lie ahead.
Part of that complexity may stem from expectations that any new contract would need to include an exit clause similar to the one included in Jamal Musiala's deal, according to recent reports.
Olise joined Bayern from Crystal Palace in 2024 for a fee in the region of €55m, and his value has since risen dramatically on the back of standout performances, with some reports putting his current worth as high as €150m. Whether his time in Munich ultimately proves to be a long-term stay or merely a stepping stone remains to be seen, but Dreesen's careful choice of words did little to settle the speculation once and for all.
The uncertainty comes despite Olise's continued excellence on the pitch, having scored in Bayern's opening-weekend win as they began the defence of their Bundesliga title in emphatic fashion.
His development under head coach Vincent Kompany has been repeatedly cited as central to his rising value, transforming him from a promising Crystal Palace talent into one of the most sought-after wingers in European football within the space of little more than a year.