BILD says the France international, with a contract to 2023, has so far rejected new terms offered by Bayern.
The winger received a contract offer from United in the summer worth €8m-a-year and he is demanding a pay-rise at Bayern to recognise his achievements with them.
United remain keen and Bayern management are concerned about losing Coman, despite him having over two years left on his deal.
"Every club wants to avoid losing a top player on a free transfer," declared Bayern chief Hasan Salihamidzic.
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