He has been included in their 18-man squad for the trip to Denmark and will at least be on the bench for the Europa League last-32 tie.
Poole left Newport County for Old Trafford in August but only recently received international clearance to feature in English football.
The 17-year-old played 15 games for the Exiles before his transfer.
Poole has been given squad number 41 by United manager Louis van Gaal, who signed the player for an undisclosed fee on the same day he paid an initial £36m for striker Anthony Martial.
Wales Under-19 defender Regan Poole could make his Manchester United debut against FC Midtjylland on Thursday.