The 20-year-old will sign fresh terms next week that will run until 2028, extending an existing deal that had been due to expire in 2027 with an option.
The move confirms Ibrahimovic will not be sold this summer.
The report credits "trusting talks" between the German Under-20 international and head coach Vincent Kompany as the key factor in reaching an agreement.
Ibrahimovic is set to stay in Munich next season, with Kompany reportedly offering him the prospect of regular playing time in attack.
The midfielder came through Bayern Munich's academy after joining from 1. FC NĂŒrnberg in 2018 and made his senior debut for the club in January 2023.
He spent the 2023-24 season on loan at Frosinone in Serie A before returning to Bayern, and had a further loan spell at Lazio in the first half of last year.
Ibrahimovic returned to Germany on loan at 1. FC Heidenheim for the 2025-26 campaign, where he scored his first Bundesliga goal from the penalty spot against Stuttgart in February.
Away from the first team, Bayern are parting company with Carsten SchĂŒnemann, head of the club's youth athletic department, according to Absolut Fussball.
The 57-year-old had held the role since the summer of 2019 but had come under heavy internal criticism in recent times.
SchĂŒnemann is said to have deliberately held back qualified athletic coaches within his department.
The club has also criticised inadequate load management under his watch, the report said.
Quirin Löppert, who joined Bayern from FC Augsburg in January as athletic and rehabilitation coach, is considered a possible internal successor.
Johannes Wieber of 1. FC NĂŒrnberg is regarded as an external candidate for the role.
Bayern's academy shake-up comes at the same time as the club move to secure the long-term future of one of its most promising homegrown talents.