The Reds are at home to Peterborough United, who beat Lincoln City and Boldmere St Michaels to reach this stage, with clubs from the Premier League and Championship now entering the competition.
Fletcher will be looking forward to taking charge of his team in the historic competition, with the tie scheduled to be played before 13 December.
Extra-time and penalties will be required to decide games after 90 minutes if the scores are level.
Fixture details will be relayed in due course, when available, including coverage of the tie.
The Under-18s' next scheduled outing, against Birmingham City, will be covered live by MUTV on Saturday 22 November.