According to his friend and France teammate Dayot Upamecano, however, Olise will be staying put in Bavaria next season.
"Did I tell Michael to stay at Bayern Munich? He's staying, he's staying," Upamecano said, smiling, after France's win over Paraguay in the World Cup last 16.
The defender's comments come amid weeks of speculation linking Olise with a switch to the Bernabeu, with reports suggesting Real Madrid have made the France international one of their top targets this summer.
Real Madrid have already issued a public statement denying any direct or indirect contact with Olise, his representatives, or his associates, stressing their respect for Bayern Munich's position.
Bayern president Herbert Hainer has also sought to play down the speculation, insisting the German champions have no intention of selling their prized asset.
"Bayern does not want to sell Michael," Hainer said, adding that Real Madrid had personally reassured him they had made no contact with the player."
Reports in Germany suggest the two clubs maintain an informal understanding never to approach a player under contract at the other without first informing them, an arrangement said to underpin their public denials over Olise.
The France winger is currently under contract at the Allianz Arena until 2029, with Bayern reportedly preparing a lucrative new deal to extend that commitment further, in part to ward off Real Madrid's interest.
Olise joined Bayern Munich from Crystal Palace in a deal worth around €60million and has established himself as one of the Bundesliga's standout performers since arriving in Germany.
Real Madrid's interest has intensified since Olise's impressive displays for France at the World Cup, with the winger contributing to his country's progress through the tournament alongside strike partner Kylian Mbappe.
Whether Upamecano's confidence is borne out will become clearer as Bayern look to finalise a new contract for their in-form attacker in the coming weeks.