The game is a rearrangement of the original fixture, which was due to have taken place earlier this month, but was postponed because of the weather.
Rangers received a bye to reach this stage, with the first team having crashed out of the competition in November after a 3-1 home defeat to local amateur side, St. Andrews.
The reserves, who play in the Humber Premier League, had beaten North Cave 2-0 in the first round, and will come up against what is expected to be a strong City side in the last eight.
First team players that played in the St. Andrews defeat won't be eligible to play, but a handful will be vying for selection, including Steve Graham, Steve Gawthorpe, Liam Cattermole, Michael Gregory and Adam Crane.
Cattermole has tasted victory in this competition before, having been part of the triumphant Tigers side that lifted the trophy with a 3-0 win against Hider Foods in 2004.
Tickets for the clash are £3 for adults, and £1 for concessions and under-16s.
Kick-off is at slightly earlier time of 7pm.