Should they get that far, they will be joined in the draw by Manchester United, who qualified after finishing fourth in the Premier League last season.
Irish club Dundalk face a big ask, going against BATE Borisov, the champions of Belarus.
The Hammers, who move to the Olympic Stadium in 2016, qualified for the competition through the fair play rule, which allocates an extra slot to the top three nations in the fair play league. They will travel to Andorra on July 2nd, before the return leg in London a week later.
Should they make the third round of qualifying they will be joined by Southampton, with Liverpool and Tottenham already in the group draw.
Scottish side St Johnstone face Alashkert of Armenia, while Aberdeen take on Macedonian side Shkendija.
Welsh sides in the draw include AUK Broughton, who meet Lokomotiva Zagreb, while Bala Town and Newtown face FC Differdange 03 of Luxembourg and Maltese side Valletta respectively.
Northern's Ireland's Glenavon play Shakhtyor Soligorsk of Belarus, with Glentoran facing Slovak side MSK Zilina.
Shamrock Rovers play Luxembourg's Progres Niedercorn, Linfield tackle NSI Runavik of the Faroe Islands and Saint Patrick's Athleticmeet Skonto FC of Latvia.
Cork City will be against KR Reykjavik of Iceland and University College Dublin face F91 Dudelange of Luxembourg.
Spanish sides are currently ruling Europe with La Liga champions Barcelona holding the Champions League, whilst Sevilla retained the Europa League.