Town’s U18s will play Liverpool or Arsenal at home in the semi-finals of the FA Youth Cup if they beat Sheffield United in their quarter-final tie.
The Blues, the only non-Premier League side still in the competition, host the Blades, who beat Bristol City 3-1 in their fifth round tie on Saturday, on a date yet to be set.
The Gunners will visit Merseyside for their tie with their date also still to be confirmed but with both matches taking place before Saturday 1st May.
Semi-final ties must be staged by Saturday 15th May, while the final will be scheduled prior to Saturday 29th May.
The other semi-final will see Newcastle United or Aston Villa at home to West Bromwich Albion or Everton.
Town's U18s, who are coached by Adem Atay and Jason Dozzell, beat Southend 4-1 at home in round one, won 5-0 away at Chelmsford in the second round, then dramatically came from behind to beat Fulham, who have a category one academy, 3-2 at Portman Road in round three.
They followed that up with a 3-1 home victory over Swindon before a 1-0 win away against another category one academy, Middlesbrough, in round five.
Town have won the competition on three occasions, in 1973, 1975 and 2005.