They will travel to EFL league two club Stockport County in the week commencing 30 October after overcoming Wythenshaw Under 18s 2-1 earlier this week.
The tie is set to take place at Edgeley Park, with further fixture details to be announced in due course.
Director of football Pav Singh and head coach Luke Dean have been the driving force behind the ETS and are proud of the fantastic start in both FA Youth Cup and the league.
Pav said: “The lads have been fantastic and continue to raise their standards on and off the pitch. Credit to Luke, who has been outstanding with the players on a day-to-day basis and a delight to coach with. Luke is a fantastic coach and the detail and prep he provides for the players is excellent.
“The recruitment of players from Clifton Robinson in the background has also been spot on and has certainly brought success so far.”
Farsley Celtic chairman Paul Barthorpe added: “I am so proud of the direction we are going as a club. It’s been a delight to see the successes of the Emerging Talent Squad and the pathway we are creating to first team is certainly building a high performance culture.”