The Hammers are due to host the first leg on 28 July, but the London club have made an official request to Uefa to reverse the dates of the two games.
That is because their stadium stages an athletics meeting - the London Anniversary Games - on 22 and 23 July.
The second leg is set for 4 August.
Five other British sides could also be involved in the third round of qualifying if they make it past round two.
Aberdeen could face either Maribor or Levski Sofia, Hearts could play Krasnodar, while Hibernian could play Hertha Berlin.
Cliftonville could face a trip to Russia to play Spartak Moscow, while Connah's Quay could face either Irish side St Patrick's Athletic or Dinamo Minsk.
All five British sides play the second legs of their second qualifying round matches on 21 July.
West Ham finished seventh in the Premier League last season and qualified for Europe courtesy of fifth-placed Manchester United winning the FA Cup.
The Hammers made the switch to the Olympic Stadium from their home at the Boleyn Ground at the end of last season.
West Ham's first competitive match at the Olympic Stadium will be against either Shakhtyor Soligorsk of Belarus or Slovenia's NK Domzale in the third qualifying round of the Europa League.