Jackson joined Bayern on loan last summer in a deal worth a £14 million fee, with a conditional purchase option of around £65 million that depended on appearance targets the player was unable to reach.
His season in Bavaria has been respectable without being decisive. He has scored nine goals and provided four assists in 28 appearances under Vincent Kompany, filling in as Harry Kane's primary backup. Kompany has been appreciative of the striker's attitude and professionalism throughout.
Despite that, the Bayern board took a different view to the coaching staff on the cost-to-benefit calculation of the deal.
Florian Plettenberg of Sky Germany confirmed: "There are currently no talks about a second loan or about a permanent deal."
Jackson is under contract at Chelsea until 2033 on a salary of around €7.5 million per year.
Chelsea are expected to place him on the transfer market immediately upon his return and will prioritise a permanent sale. AC Milan, Juventus and Napoli have all been credited with interest, as have several Premier League clubs.
The Sun reported this week that Jackson is open to returning to Stamford Bridge and has been in contact with teammates Enzo Fernández and Moïses Caicedo, though he plans to make no final decision until after the World Cup, where he will represent Senegal.