The Cottagers, who will play in Europe for the first time in seven years, were drawn to play either Finnish side HJK Helsinki or Lithuanian outfit FK Vetra.
HJK will be favoured to progress against Vetra, however - they take a 1-0 advantage into the home leg of their second qualifying round tie - meaning that Hodgson looks likely to return to the nation whose national side he managed prior to joining Fulham.
New Aberdeen boss Mark McGhee will have to wait to discover the opposition he will face in his first competitive game in charge.
The Dons were drawn against 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
