The final batch of home tickets went on sale at 6pm on Monday.
A block in the North Stand became available, along with seats not taken up by season ticket holders across the three stands.
United described the reaction as "astonishing" and there were fewer than 500 tickets in home areas at 9.30am, when the ticket office opened to take bookings in person and on the phone.
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They are expected to be snapped up today, as Saturday's tie - United's first at this stage of the competition since 1999 - is on course for another bumper attendance.
Blackburn Rovers have reported they have about 300 tickets remaining from their 1,500 allocation.
In the previous round 11,673 watched the 3-2 win against Swansea City, which was the biggest home gate for almost four years.