Goretzka, 26, is currently at a similar stand-off over his future with Bayern Munich.
The former Schalke ace could be available on a free transfer in a year's time or – if there is no resolution – may have to be sold for a knockdown fee this summer.
New Bayern boss Julian Nagelsmann has made it clear he wants an agreement to be found.
But United will continue to monitor developments in the hope they could land a ready-made replacement for Pogba, who is a summer target for PSG.
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