The Sun says the 32-year-old could move to his former club for free, provided United agrees to a severance payment.
The attacking midfielder still has a contract with United until 2025.
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United will have to cut some players from the payroll to finance planned changes.
The only possibility of him staying would be if Mauricio Pochettino, Eriksen's old mentor from his Tottenham days, were to replace Erik ten Hag as manager at United.