2:21PM BST 15 Jul 2011
The teams were paired together in today's draw in Nyon, with the first leg taking place at the Britannia Stadium on July 28 before the FA Cup runners-up travel to Split on August 4.
Fulham, who are 3-1 up on Crusaders after yesterday's first leg, are also likely to face a team from the Croatian city, with RNK Split leading Domzale of Slovenia 2-1 heading into their home match.
Hearts will meet Hungarian side Paksi or Tromso of Norway while a clash with either Metalurg Skopje of Macedonia or Bulgaria's Levski Sofia awaits Dundee United if they can overturn a 1-0 first-leg deficit to Slask Wroclaw.
Hajduk are likely to provide stiff opposition for Stoke City and possess an impressive European pedigree.
They have reached the quarter-finals of the European Cup three times, most recently in 1994-95, while they were semi-finalists in the Uefa Cup in 1983-84.