The heavyweight duo, who meet in a league match at Headingley on Friday night, were paired together in the draw for the semi-finals.
Saints, who won the cup in three successive years from 2006, were the final team to secure their place in the last four, courtesy of a 36-20 win over Widnes at Langtree Park on Sunday afternoon.
Makeshift full-back Mark Percival scored two of his side’s six tries as Saints came from behind, finishing strongly against their tiring opponents, to clinch a first semi-final appearance for four years.
Brian McDermott’s Leeds were impressive winners over Hull.
In the other semi-final, Warrington will take on Hull KR, who are aiming for a first Cup final appearance since 1986.
Draw: Leeds v St Helens, Warrington v Hull KR.
Ties to be played on Friday, July 31 and Saturday, August 1.