The tie is nicely poised following a 1-1 draw in the first leg, and the winners will face Cyprian outfit Apollon Limassol in the third qualifying round.
Match preview
After summer signing Philip Zinckernagel had given Olympiacos a seventh-minute lead in the first leg, the Red-Whites were seemingly on course to hold on for a slender win. However, a 92nd-minute equaliser from Dolev Haziza rescued a draw for the hosts.
Pedro Martins will have been disappointed to have seen his side concede so late in the game and to miss out on taking a one-goal advantage into the second leg, but nevertheless, they remain in the tie and will have the support of their passionate home crowd for Wednesday's fixture in Piraeus.
Olympiacos, who cruised to their 47th Greek Super League title by 19 points last season, are yet to begin the defence of their top-flight crown this term, but took part in eight pre-season friendlies before their first-leg clash with Maccabi Haifa.
The Red-Whites, however, struggled to build a positive run of form over the summer as they only won two of their eight warm-up matches, losing four and drawing the other two.
Olympiacos will look to put their pre-season form to one side and instead reflect on their impressive home form over the last 12 months, which has seen them lose only three of their last 28 competitive matches at the Karaiskakis Stadium.
Maccabi Haifa, meanwhile, ended a four-game losing run across all competitions with the 1-1 draw against Olympiacos in last week's first leg.
The Greens had previously lost the Israeli Super Cup on penalties to Hapoel Be'er Sheva after suffering back-to-back 1-0 defeats in pre-season against Mechelen and Vitesse.
Head coach Barak Bakhar will be keen for performance levels to improve, although their fightback to rescue a draw against Olympiacos is at least one positive to take from last week and hopes of reaching their first Champions League group stage since 2009-10 remain alive.
Bakhar has history against Olympiacos following his time in charge at Be'er Sheva, who secured a 1-0 aggregate victory over the Greek giants to progress to the Champions League playoff round in 2016-17.
Olympiacos Champions League form:
Olympiacos form (all competitions):
Maccabi Haifa Champions League form:
Maccabi Haifa form (all competitions):
Team News
Olympiacos boss Martins has a large squad at his disposal and will be required to make some big calls over who is named in the starting lineup and who misses out.
Summer signings Sime Vrsaljko and Pipa will battle for a place at right-back, while former Arsenal defender Sokratis Papastathopoulos will be hoping to force his way into the first XI ahead of either Kostas Manolas or Pape Abou Cisse.
Midfielders Mady Camara, Pierre Kunde and Mathieu Valbuena all began on the bench in the first leg and will be looking to return to the starting lineup on Wednesday, while Tiquinho Soares faces competition from Youssef El Arabi to keep his place up front.
As for Maccabi Haifa, midfielder Mahmoud Jaber is ruled out with a thigh injury which he sustained in the Israeli Super Cup earlier this month.
As a result, former Queens Park Rangers midfielder Tjaronn Chery is set to continue in the middle of the pitch, playing alongside captain Neta Lavi and Ali Mohamed.
Omer Atzili, Dean David and Haziza - who scored a combined 62 goals across all competitions last season, with the former netting 28 of those - are all set to continue in attack, although summer signing Nikita Rukavytsya will also be in contention for a place up front.
Olympiacos possible starting lineup:
Vaclik; Vrsaljko, Manolas, Cisse, Reabciuk; M'Vila, M. Camara; Masouras, A, Camara; Zinckernagel; El Arabi
Maccabi Haifa possible starting lineup:
Cohen; Sundgren, Goldberg, Planic, Menahem; Lavi, Mohamed, Chery; Atzili, David, Haziza
We say: Olympiacos 2-0 Maccabi Haifa (Olympiacos to win 3-1 on aggregate)
Both sides have endured inconsistent runs of form in recent weeks, but they will be confident in their own abilities to come out on top and progress to the next round.