Celtic will almost certainly face off against the Finnish outfit for the second time in their history, having beaten them 3-2 on aggregate in the early stages of the 2000/01 UEFA Cup. HJK won the first leg of their second qualifying round clash against KR Reykjavik 7-0.
Motherwell, who were granted entry into the competition due to the liquidation of Rangers, will face Athens club Panathinaikos, who were runners-up in the Greek super League last season.
League of Ireland winners Shamrock Rovers know that only Belgian club Anderlecht will stand between them and a place in the play-offs if they can defeat Lithuanian side Ekranas, with whom they drew 0-0 in their first leg at the Tallaght Stadium.
Northern Ireland champions Linfield will face either Maltese outfit FC Valetta or Serb club Partizan Belgrade if they come through their second-tie against AEL Limassol of Cyprus, where they lost the first leg 3-0.
Likewise, Welsh champions The New Saints' reward if they beat Swedish club Helsingborgs – who they held to a goalless draw at home in their first leg - will be a tie against either Buducnost Podgorica of Montenegro or Slask Wroclaw of Poland.
The return legs of all the second qualifying round ties will be played on July 25 and 25, with the third round matches taking place on July 31-August 1 and August 7-8.