The cup clash will take place at Whitley Park, with United's second string attempting to reach the last four of the tournament for the first time.
Ben Dawson's side advanced into the last eight for the third consecutive season as goals from Jamie Sterry and Tom Allan secured a 2-1 away victory against Reading.
The Rams sit in third place of Division One in Premier League 2 - one tier above the Magpies.
However, the youngsters will be looking to continue their positive winning run of late, after defeating the Royals at Woking's Kingfield Stadium along with an impressive 2-0 win over Division Two leaders Wolves on Saturday.