Cottagers boss Roy Hodgson could be set for a return to Finland after the draw was made in Nyon on Friday.
Fulham, who will play in Europe for the first time in seven years, were drawn to play either Finnish side Helsinki or Lithuanian outfit Vetra to open up the possibility of the former Finland manager returning to the Nordic country.
HJK will be favoured to progress against Vetra, who they host in the second leg of their second qualifying round tie next week holding a 1-0 advantage.
New Aberdeen boss Mark McGhee will have to wait to discover the opposition he will face in his first competitive game in charge after the Dons were drawn against either Czech Republic club Sigma Olomouc or Fram, who currently sit eighth in the Icelandic league.
Sigma, who finished fourth in the Gambrinus Liga last season, must recover from a surprise 1-1 draw at home last week if they are to progress.
Falkirk will definitely face Czech opposition, in the form of Slovan Liberec, in the next round if they can defend their 1-0 advantage against FC Vaduz.
Last year's beaten Scottish Cup finalists are favourites to progress after Ryan Flynn scored the only goal of the first leg, meaning a draw in the Liechtenstein capital will be enough to see
them through on Thursday.
Motherwell will face another trip to eastern Europe if they can overcome a 1-0 deficit against Albanian side KS Flamurtari in their second qualifying round tie.
Jim Gannon's side, who were knocked out by Nancy in the first round of the UEFA Cup last term, were drawn to play either Romania's Steaua Bucharest or Ujpest of Hungary.
The matches for the third qualifying round will be played on July 30 and August 6.