Bayern sporting director Max Eberl confirmed the news on ZDF on Saturday, stating simply: "We will not trigger the option for Nicolas Jackson."
The clause would have been activated had Jackson featured for at least 45 minutes in 40 matches, but with Harry Kane producing 53 goals and six assists this season, the Senegalese striker was limited to a supporting role and made only 13 starts.
Newcastle's interest has been reported by talkSPORT. The Magpies need a recognised centre-forward following the failure of Nick Woltemade and Yoane Wissa to provide adequate cover after Alexander Isak's record £130 million move to Liverpool last summer.
Chelsea are expected to pursue a permanent sale. Jackson is under contract until 2033 and earns around €7.5 million per year, a wage Chelsea would be keen to remove from their books particularly if they fail to qualify for the Champions League. His value is estimated at around £40 million.
The relationship between player and club is understood to be strained. Chelsea nearly cancelled his Bayern loan at the 11th hour last summer when Liam Delap picked up an injury, before eventually allowing him to leave after recalling Marc Guiu from Sunderland to provide cover.
AC Milan, Juventus and Napoli have also been credited with interest.