The Hammers achieved automatic qualification after finishing sixth in the Premier League last season, while their hosts fell short in the qualifying rounds for the Champions League
After winning the Croatian top flight for the fourth straight season last time around, earning 85 points from 36 outings, Dinamo Zagreb booked their place in Champions League Qualifying, and they started well in the first round.
They met Icelandic side Valur Reykjavik and cruised through with a 5-2 aggregate win, before comfortably defeating Cypriot champions Omonia 3-0 over two legs to reach the third round.
A Bartol Franjic goal then fired them to a 1-0 away win over Legia Warsaw, sealing a 2-1 aggregate win and putting them one two-legged affair away from the group stage, but Damir Krznar's side would miss out.
The Modri met Moldovan champions Sheriff in the playoff round, and they were unable to overturn a 3-0 deficit from the away leg as the second leg ended goalless.
As a result, they dropped into the Europa League group stage, and will look to build on a strong start to the domestic season, having collected 16 points from their opening seven games, with what would be an impressive opening victory.
They will also hope to replicate last season's showing in the Europa League, as they staged an eye-catching comeback against Tottenham Hotspur to seal a 3-2 aggregate victory after a 2-0 away defeat, reaching the quarter-final before they were knocked out by eventual winners Villarreal.
West Ham arrive to play competitive football in Europe for the first time since the 2016-17 season, when they lost 2-1 to Astra Giurgiu in the Europa League playoff round.
The London side did not have to go through qualifying this time around though, as their sixth-placed finish in the Premier League saw them earn automatic progression to this year's competition.
David Moyes's men defied the odds to collect 65 points last season, pipping Tottenham Hotspur to sixth spot, and they began the new domestic season in style.
Goals from Aaron Cresswell, Said Benrahma, Tomas Soucek and Michail Antonio fired the Irons to a 4-2 away win over Newcastle United on the opening day, before they comfortably defeated last season's fifth-placed side Leicester City, with Antonio hitting a brace alongside goals from Pablo Fornals and Benrahma in a dominant 4-1 victory.
Moyes's side now come into Thursday's game on the back of consecutive draws, most recently playing out a stalemate with Southampton, and they will hope to mark their return to continental football with an away victory.
West Ham United forward Michael Antonio was sent off at the weekend, but he will be available to play in Croatia, with the suspension instead carrying over to the Premier League.
Croatian attacking midfielder Nikola Vlasic is also set to be handed his full debut on home soil, giving Benrahma a brief rest before their return to league action at the weekend.
Dinamo Zagreb possible starting lineup:
Zagorac; Lauritsen, Sutalo, Theopile-Catherine; Ristovski, Ademi, Misic, Franjic; Orsic, Petkovic, Ivanusec
West Ham United possible starting lineup:
Areola; Fredericks, Zouma, Ogbonna, Johnson; Kral, Noble; Yarmolenko, Vlasic, Bowen; Antonio
We say: Dinamo Zagreb 1-1 West Ham United
In what should certainly be a closely-fought encounter, we see Thursday's game finishing level in a result that will be relatively pleasing to both sides.
The firepower of West Ham's front line should see them escape with a result, despite Moyes potentially calling on several squad players.