The Bantams booked their place in round two last Monday thanks to a 2-0 win at Scunthorpe United but they have had to wait until this Tuesday before finding out their next opponents in the competition.
Morecambe secured their date with City thanks to a 3-1 home win over Pools at the club's main Globe Arena.
In line with F.A Youth Cup competition rules, City's match at Morecambe will also be played at the Globe Arena. No date for the tie has been confirmed as of yet but it must be played by Saturday 23 November 2013.
As well as still being active in this season's F.A Youth Cup, City's apprentices currently sit top of the North East Youth Alliance division after eight straight wins from their first eight league fixtures.
After defeating Lincoln City 6-2 last Saturday, City are six points clear at the top with a goal difference of plus 23. They have scored 31 goals in total in their opening eight league games for the season.
With the club's youngsters also through to the second round of the Football League Youth Alliance Cup thanks to a penalty shoot-out win over Scunthorpe, City have actually emerged victorious from EVERY match they have played so far this campaign.