Osmani, who was born in Munich and has come through Bayern's youth ranks since 2017, made his first-team debut in March in a 4-0 win over Union Berlin and will continue to train regularly with Vincent Kompany's senior squad alongside his development with the youth sides.
Jochen Sauer, Bayern's director of academy development, said: "Erblin is a born Munich lad and a genuine FC Bayern academy product. He has already made his debut with our first team and we are convinced of his further development potential. We are pleased that Erblin will continue taking the next steps together with us."
While that piece of business is done, Bayern Munich's bigger concern this summer is holding onto Olise.
Fussballtransfers.com revealed in mid-July that the 24-year-old wants to leave for Real Madrid this year, a report since corroborated by Sport Bild, which says France team-mate Kylian Mbappe has played a decisive role in driving Olise's desire to move.
According to Sport Bild, Mbappe – who is close friends with Olise – courted his international colleague throughout the World Cup, talking up how the pair could combine on the pitch at the Bernabeu and stressing that Real "urgently need him."
Mbappe reportedly also talked up Madrid's restaurant scene and climate, with Olise said to be receptive to the pitch before Mbappe relayed the positive signals to Real president Florentino Perez.
A new contract at Bayern has not been ruled out. Sport Bild reports that the club are considering an improved offer that would take Olise's salary from €14m to €25m a year, though those figures have not been independently corroborated beyond the German outlet's reporting.
Ultimately, Bayern's hopes of keeping Olise are likely to hinge on the club's ability to convince him they can compete for the Champions League with a squad capable of winning it — an area over which the forward is said to have doubts.
Olise is said to want face-to-face talks with the Bayern hierarchy in the near future and to be shown a concrete plan for how the club intend to close that gap.