Mourinho is believed to be frustrated by what he sees as a lack of leadership and aggression in his defence as United struggle for consistency this season.
The manager is understood to have put together a list of priority targets for the January transfer window, with £30m-rated Dutchman Van Dijk at the top.
United’s soft centre has been exposed in the early weeks of the campaign with Chris Smalling, Luke Shaw and Daley Blind all coming in for criticism, while Marcus Rojo is also expected to be dropped.
Van Dijk is regarded as the ideal solution to the problem; at 25 years old he is a powerful figure and would add the leadership Mourinho feels he is lacking.
United face a crucial clash against Swansea on Sunday afternoon having won just once in their last four games.
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