The young Magpies travel to Woodhorn Lane to take on the Northern League Division One outfit for a place in the semi-finals of the competition, with kick-off taking place at 7.30pm (GMT).
United's youngsters booked their spot in the last-eight following a 3-1 victory against Newcastle Benfield in round one while Ashington, who compete in the ninth tier of English football, claimed a 3-2 win against Blyth Town.
Newcastle's second-string have won the trophy a record 38 times, with their most recent cup triumph coming back in 2018 after defeating Morpeth Town 3-1 at St. James' Park.
Techflow Marine Senior Cup quarter-final draw:
Bedlington Terriers vs Newcastle University
Ashington vs Newcastle United U23
Morpeth Town or Whitley Bay vs Blyth Spartans
North Shields vs Heaton Stannington