Lee Radford’s side - winners in 2016 and 2017 - head to prolific Super League leaders St Helens in the quarter-final stages.
Ironically, Saints are the only side to have won the competition three years running in the summer era.
But Hull, who won 38-20 at Championship club Featherstone Rovers on Thursday, have made it one of their prime targets this term.
St Helens showed their class once more in knocking out Castleford Tigers with a 36-18 success at Wheldon Road on Saturday, Australian full-back Ben Barba grabbing a spectacular hat-trick.
Leeds Rhinos, meanwhile, are in the unusual position of securing a home draw in the last eight but having to now play at a neutral venue - Featherstone’s LD Nutrition Stadium.
Brian McDermott’s side will face the last remaining Championship club Leigh Centurions who knocked out Super League Salford Red Devils on Friday.
However, the quarter-finals are due to take place from Thursday May 31 to Sunday June 3.
Emerald Headingley host the second cricket Test match between England and Pakistan from Friday June 1 but independent security protocol means that the stadium is not allowed to be used the night before the match begins.
With England’s football side playing their final friendly prior to the 2018 FIFA World Cup at Elland Road against Costa Rica on Thursday June 7 it means the Rhinos have had to look outside of the city to host the Challenge Cup clash.
But, given they have a long-standing partnership with Featherstone as part of the dual-registration process and play at Post Office Road each pre-season, they have struck a deal with their fellow West Yorkshire club to host the game there.
In other ties, Huddersfield Giants, who beat Super League rivals Wakefield Trinity on Friday, will host Catalans Dragons and Warrington Wolves entertain Wigan Warriors.
Warrington, the form team in Britain at the moment, eased their way into the last eight with yesterday’s one-sided 66-10 victory over Championship leaders Toronto Wolfpack.
It was their tenth successive win in all competitions and served as a sobering lesson for the big-spending but wildly ill-disciplined Canadian outfit who have ambitions of earning promotion to Super League for 2019.
Wigan reached the quarter-finals after winning 28-10 at 12-men Hull KR.
Rovers saw former Wigan second-row Danny Tickle red-carded just before half-time after punching England’s John Batemen but they fired back from behind to draw level 10-10 on the hour mark.
It was only late on that the visitors pulled away.
St Helens v Hull FC
Leeds Rhinos v Leigh Centurions
Huddersfield Giants v Catalans Dragons
Warrington Wolves v Wigan Warriors