United's youngsters booked their place in the last eight of the competition following a 3-1 victory against Newcastle Benfield at Whitley Park, courtesy of Stan Flaherty's brace and a goal by a trialist.
The young Magpies have been rewarded with a trip to Woodhorn Lane to take on the Northern League Division One outfit, who compete in the fifth tier of non-league football, after the Colliers claimed a 3-2 home win over Blyth Town in round one.
A date and kick-off time for the quarter-final tie will be confirmed in due course.
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