So with just under a month to go until the draw is being made, here's a look at who we could face in the first round. We're seeded for this round (along with Hearts), but should we progress, we won't be. Hearts due to their coefficient will still be seeded in the second round.
Unseeded teams coef.
Ordabasy Shymkent Kaz 3.575
CS Fola Esch Lux 3.550
Cliftonville Nir 3.400
Rudar Pljevlja Mon 3.225
HB Torshavn Far 3.225
Chikhura Sachkhere Geo 3.125
EL13 Slo 3.125 - 3.375
Shirak Gyumri Arm 3.075
Buducnost Podgorica Mon 2.975
Kapaz Ganja Azb 2.975
Birkirkara Mlt 2.966
Shkendija Tetovo Mac 2.950
Víkingur Far 2.725
MTK Budapest Hun 2.475
Hibernians FC Mlt 2.466
Spartak Myjava Svk 2.400
Suduva Marijampole Lit 2.175
RoPS Rovaniemi Fin 1.980
FK Jelgava Lat 1.825
Teuta Durrës Alb 1.825
Valur Reykjavik Isl 1.750
IFK Mariehamn Fin 1.730
FC Lusitanos And 1.699
Atlantas Klaipeda Lit 1.675
Samtredia Geo 1.625
Spartaks Jurmala Lat 1.575
Partizani Tirana Alb 1.575
Banants Yerevan Arm 1.575
NSI Runavik Far 1.475
FK Trakai Lit 1.425
Radnik Bijeljina Bos 1.425
Sloboda Tuzla Bos 1.425
Glenavon Nir 1.400
Cork City Irl 1.340
EL1 Sma 1.316
Bala Town Wal 1.200
Sileks Kratovo Mac 1.200
UE Santa Coloma And 1.199
EL13 Lux 1.050 - 2.050
Bokelj Kotor Mon 0.975
Balzan FC Mlt 0.966
Infonet Tallinn Est 0.850
Folgore Sma 0.816
Llandudno FC Wal 0.700
Connah's Quay Wal 0.700
Europa FC Gib 0.200
CW Kos 0.000
Edit: original had some errors in it. Updated list now in place, still some nice tasty possible fixtures, not sure if this is the completed list as i think some countries cup comps are still to be completed.
The legs are to be played 30/6 and 7/7.