The Athletic claims that the midfielder is ready to sign a three-year deal at Old Trafford.
Eriksen made a remarkable return to football in January after suffering a cardiac arrest playing for Denmark at last summer's European Championships.
The 30-year-old spent the second half of the 2021-22 campaign at Brentford - helping them to a creditable 13th-place finish in their maiden Premier League season.
Eriksen has been weighing up his options since departing the Bees.
But the ex-Inter Milan star is reportedly set to link up with Man Utd and work with new manager Erik ten Hag.