The teams contest the first leg of their second qualifying round tie with the Israeli champions seeking to edge closer towards a group stage appearance for the first time in over a decade; their Greek counterparts last made it that far two years ago.
Match preview
Having come close in both the 2018-19 and 2019-20 Israeli Premier League seasons, Maccabi Haifa ended their 10-year wait for their domestic title by finishing four points clear of Maccabi Tel Aviv last year, before successfully defending their crown by an eight-point margin in May.
They therefore earned another crack at Europe's top club competition, but the Greens have not reached the group phase since 2010, having lost in the first qualifying round to Kazakhstan's Kairat last summer.
Following this week's draw, a third round encounter with Apollon Limassol awaits the winner of Haifa's tie against Olympiacos, but preparations for their continental campaign have not run smoothly.
Friendly losses to Mechelen and Vitesse Arnhem earlier this month were followed by a penalty shootout defeat in the Israeli Super Cup final on Saturday, when they were beaten by Hapoel Be'er-Sheva - and the 14-time national champions have scored only once in the process.
Haifa head coach Barak Bakhar will undoubtedly be concerned, but he actually steered Be'er-Sheva into the 2016-17 Europa League by overcoming Olympiacos 1-0 on aggregate. Having then done the double over Inter Milan during the group stage, the 42-year-old certainly has some pedigree in UEFA competition.
If Haifa's championship win was impressive, then Olympiacos dominated their domestic rivals even more last term: cruising to the Greek Super League title by 19 points, ahead of closest challengers PAOK.
After just a few weeks away, the Erythrolefki reconvened in late June, taking part in a series of friendlies against sides such as Fortuna Dusseldorf, Slavia Prague and RB Salzburg - losing 3-1 to the latter at the start of the month.
The Piraeus club's friendly most recent warm-up match came against Aris last Monday, and after a 2-1 defeat, coach Pedro Martins was critical of his side's defensive concentration.
If they are to return to the Champions League proper, that aspect of their game must surely improve, and they will be doubly determined to qualify this time after losing in the third round last year to Bulgaria's Ludogorets.
In European competitions, perhaps the finest hour for Olympiacos came when they reached the quarter-finals in 1999, only missing out on the semis in the final minutes of their tie with Juventus. Replicating that achievement this year, however unlikely, relies on them first pushing past Haifa in the coming days.
Maccabi Haifa form (all competitions):
Olympiacos form (all competitions):
Team News
After offloading misfiring forward Henry Onyekuru to Adana Demirspor on loan, Olympiacos will again rely on Brazilian striker Tiquinho Soares to lead their attacking threat on Wednesday.
Although Brazilian side Botafogo have declared an interest in signing the 31-year-old this summer, he remains in Piraeus and could join Youssef El-Arabi up front.
Former Sevilla goalkeeper Tomas Vaclik will start as the visitors' last line of defence, with another experienced European campaigner, Kostas Manolas featuring in the back four.
Meanwhile, Maccabi Haifa's hopes of progression took a blow when midfielder Mahmoud Jaber suffered an injury against Hapoel Be'er Sheva at the weekend, and the Israel international will now miss both matches against Olympiacos.
In his absence, the hosts will most likely turn to captain Neta Lavi and Surinamese midfielder Tjaronn Chery to run their engine room, while Nikita Rukavytsya and Frantzdy Pierrot battle it out to start up front.
Maccabi Haifa possible starting lineup:
Cohen; Sundgren, Goldberg, Planic, Menahem; Lavi, Mohamed, Chery; David, Rukavytsya, Atzili
Olympiacos possible starting lineup:
Vaclik; Vrsaljko, Ba, Manolas, Reabciuk; Bouchalakis, Kunde; Masouras, Valbuena, Tiquinho; El Arabi
We say: Maccabi Haifa 1-2 Olympiacos
Though it has not always gone to plan in terms of results, Olympiacos have prepared thoroughly for their latest Champions League campaign, and they have enough attacking talent to score at least once on Wednesday. Haifa have proved even more sluggish in pre-season, so may end up trailing before next week's return leg.