The Swiss midfielder is set to leave Borussia Monchengladbach when his contract expires in the summer.
United had been viewed as the favourites to sign Zakaria on a free transfer.
Bayern want to take advantage of this fact as sporting director Hasan Salihamidzic has been following Zakaria for a number of years.
Zakaria is viewed as an ideal replacement for Corentin Tolisso, who is expected to depart the Allianz.
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