The France international is now inside the final 12 months of his current Bayern deal.
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BILD's Christian Falk is reporting United are lining up a move for Upamecano.
Bayern Munich is pushing to extend his contract - but that no major progress has yet been made.
However, the defender himself recently hinted that an agreement could soon be struck.
"I'm really happy here. There are now talks with Max (Eberl), Christoph (Freund) and my agent. We'll see what happens," he said.