According to transfer expert Ben Jacobs, the 25-year-old has given the Bavarian the green light to complete the transfer, with both parties now aligned on personal terms.
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Gordon is understood to be open to joining the Bundesliga champions, viewing the move as an attractive next step in his career.
However, negotiations between the clubs remain complicated due to Magpies’ £80 million (€92m) asking price.
Bayern’s current financial strategy focuses on controlled spending, with sporting directors Max Eberl and Christoph Freund instructed to strengthen key areas without major outlays.
Club president Uli Hoeneß reportedly supports the move, but Bayern are expected to push for a reduced fee as talks between the two clubs continue.