Hojlund has insisted he wants to stay at Old Trafflord for the new season.
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But BBC Sport says United are prepared to sell the Denmark striker before the market shuts and have set a price of £30m.
Hojlund, formerly of Atalanta, has been linked with a return to Serie A, where champions Napoli and Juventus are interested.
United need to sell before they buy again this summer and Hojlund can be moved on if they reach an agreement for a new centre-forward addition.
Hojlund scored twice in United's preseason win against Bournemouth last week.