United have been allocated 6,000 tickets for the January 8 trip to Stamford Bridge in the third round of the famous competition, and look like filling most of that allocation.
Season ticket and loyalty card holders and supporters club members were the first to be able to secure their place.
It looks set to be United's largest away following since the play-off final at Wembley in 1999, even eclipsing the large numbers who went to Bolton and Portsmouth in recent seasons.
Tickets are priced at £25, with £12 concessions. They remain on restricted sale on Friday and Monday before going on general sale from Tuesday.
Space on the coaches cost £14, with executive coaches costing £17. Ten have already been filled.
Telephone orders will not be taken on Tuesday, with priority given to fans who queue at Glanford Park.