Jackson, 24, joined Bayern Munich in dramatic fashion on transfer deadline day last summer, but has struggled to make an impression.
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The striker has started just three Bundesliga game for the German giants, scoring five goals in 22 appearances across all competitions.
According to The Times, Bayern have informed Chelsea that they have no intention of activating the £56 million option to buy in their loan deal.
As a result, Chelsea are now open to reintegrating Jackson into the first team now that Liam Rosenior is their new head coach.