The draw was made on Saturday afternoon and the young Magpies were paired against their local rivals, who are currently challenging for promotion from League One.
Ben Dawson's under-21 side are one of only three Academy teams to reach the last 16 after beating Doncaster Rovers (3-1), Notts County (2-0) and Grimsby Town (3-2) in the group stages before overcoming Macclesfield Town on penalties after a 1-1 draw in round two.
Jack Ross' Black Cats, meanwhile, drew 0-0 with Stoke City's under-21s in their first group game before beating Carlisle United 3-1 and Morecambe 1-0 to secure qualification from Group A. They then beat Notts County 2-0 in the second round.
Last 16 ties will be played in the week commencing 7th January 2019. Ticket news will be announced in due course.