A number of clubs are thought to have expressed an interest in Hojlund, 23, in the knowledge United are willing to negotiate over his release.
It is understood Milan are keen, although they would only want a loan initially as they, like United, are hindered financially by an absence from European competition this season.
Sources suggest the Serie A side are willing to pay an initial 4m euros (£3.47m) loan fee, with an additional option to buy next summer for 40m (£34.7m).
Whether that is acceptable to United is open to doubt, although it is anticipated there will be more clarity on the situation in the coming week.
Milan open their Serie A campaign against Cremonese on 23 August.
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