Khedira, who spent five years at Real Madrid between 2010 and 2015, winning the Copa del Rey and playing alongside some of the club's greatest players, made his case emphatically.
"He is perfect for Real Madrid," the World Cup winner told AS. "If Real Madrid do not consider him seriously, it would be very strange. Real Madrid do not want to spend a lot of money on established older stars.
"They prefer to invest in developing players who have at least six or eight years of career ahead of them. At 24, Olise meets these requirements. He offers a complete solution and fits perfectly with the club's vision."
The numbers back the enthusiasm. Olise has accumulated 16 goals and 28 assists in 40 appearances across all competitions for Bayern this season — figures that place him among the most productive attackers in European football. London-born but a French international, he joined Bayern from Crystal Palace for €60 million in the summer of 2024 and has been outstanding ever since, earning the Bundesliga's Rookie of the Season award in his debut campaign before stepping up further this term.
Real Madrid president Florentino Pérez is said to be a serious admirer, with reports suggesting a potential bid of up to €160 million is being discussed internally. Liverpool have also made concrete approaches, with one reported offer in the region of €150 million turned down. Kylian Mbappé has reportedly lobbied Madrid's sporting department directly to sign his France team-mate.
Bayern's position, however, remains immovable. Sporting director Max Eberl has stated publicly that Olise is not for sale at any price, and the club are working on a contract extension to keep him at the Allianz Arena beyond his current deal until 2029. For now, Madrid and the rest of Europe's elite are simply watching and waiting.