The reward for lead coach Travis Binnion's side is a trip to the Select Car Leasing Stadium to take on the young Royals.
Reading defeated Bromley in the previous round, winning 3-1 on the road after the tie went to extra time.
The game is set to be played on Thursday 13 January, with kick-off at 19:00 GMT.
Ticket details and clarification of MUTV coverage of the action will be provided in due course. The tie must be decided on the night with extra-time and penalties coming into effect, if required.