The 25-year-old forward made 34 appearances for the Bavarians in all competitions during the 2025/26 campaign, scoring 11 goals and providing four assists as the club won the domestic double for the 14th time in their history.
However, he played second fiddle to England striker Harry Kane, confining him to feature mostly as a substitute under Vincent Kompany.
According to reports, the German giants were not prepared to pay the €50million option to buy the Senegalese goalscorer despite Belgian coach Kompany being happy with the players contribution.
The player is expected to Chelsea following Senegal's elimination from the FIFA World Cup Round of 32, with the club expected to make signings to boost new manager Xabi Alonso's squad following a disappointing 2025/26 Premier League campaign.
Jackson has played 81 matches for the Blues, scoring 30 goals and providing 12 assists following his move from Villarreal.