The Daily Express says United are exploring the prospect of tempting the Argentina international to Old Trafford this coming summer.
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Mac Allister, 27, has a deal with Liverpool to 2028, but is weighing up his options, with his father and agent, Carlos Mac Allister keeping the door ajar to a move to Real Madrid just last week.
United, with plans to rebuild their midfield, are also interested, though Mac Allister would risk running a gauntlet through Merseyside to get to Manchester.
Not since Phil Chisnall's 1964 switch from United to Liverpool has a player transferred directly between the two clubs.
However, United's hand would be strengthened should they finish in the top four and qualify for the Champions League and Liverpool miss out.