While the Eagles are already through thanks to last week's win over Juventus, they trail Paris Saint-Germain on goal difference after drawing both meetings with the French club 1-1. Their hosts, meanwhile, need points to pip Juve to a place in the Europa League.
Match preview
Just days after beating title rivals Porto in the Primeira Liga, a relentless Benfica side welcomed Juventus to Estadio da Luz last week, seeking to secure the double over their Italian counterparts and seal a place in the Champions League's last 16.
In keeping with their scintillating form this term, the Lisbon club roared into a 3-1 lead before half time, as Antonio Silva opened the scoring, then Joao Mario and Rafa Silva found the net following a Juve equaliser.
The latter then doubled his tally with a 50th-minute strike - effectively killing the game - before the hapless visitors struck back twice late on, to reduce their deficit to a single goal. Benfica held on, though, for a 4-3 win.
Roger Schmidt's side have now picked up 11 points from five Group H fixtures to sit second, just behind first-placed PSG on goal difference. Impressively, the former Bayer Leverkusen boss has personally lost none of his last 13 group stage matches.
After extending their unbeaten run to 20 games, the Eagles added one more to their tally on Saturday: having finished third in last season's Primeira Liga, they currently hold top spot in the table - now six points clear after thumping Chaves 5-0.
As a measure of their success in Europe, too, Benfica have qualified for the Champions League knockout phase for only the second time in their last five attempts, after doing so last year, when they pushed Liverpool all the way in the quarter-finals. With the last-16 draw to be held next Monday, thoughts will soon be turning to whether they can perhaps go even further.
Their autumn form suggests they are live contenders, as the two-time European champions are on their best run in the competition since between 1988 and 1990: if they now beat Haifa, a new club record for most points in the Champions League group stage will be set.
In their only previous meeting with Benfica, back on the opening matchday, a 2-0 loss in Lisbon set the tone for Maccabi Haifa's campaign, in which they have been beaten four times out of five; conceding 15 goals in the process.
Following a momentous 2-0 victory over fallen giants Juventus, though, in their most recent home match, they are now aiming to record consecutive home wins in European competition for the first time since October 2011.
While that success went down in the record books, and provided a small glimmer of hope, Barak Bakhar's side conceded seven in Paris last time out and definitely cannot reach the last 16; furthermore, Haifa have now lost 13 of their 17 matches in the Champions League group phase.
However, in the contest for a Europa League playoff place, Juve are currently third only on goal difference (-3 to -9), as both teams beat each other by a two-goal margin. That leaves the door marginally ajar, as an improbably big win over Benfica and a similar victory for PSG would see the Israelis stay in continental competition.
Even if they bow to the apparently inevitable and make their exit on Wednesday, Haifa have already taken several steps toward booking their return ticket for next year: at the weekend, a 3-1 win over Ashdod put them ahead of Maccabi Tel-Aviv at the top of the domestic standings.
Maccabi Haifa Champions League form:
D
L
L
L
W
L
Benfica Champions League form:
W
W
W
D
D
W
Benfica form (all competitions):
D
W
D
W
W
W
Team News
Though his side are already through, Roger Schmidt's preference for continuity should see him name a familiar XI on Tuesday.
An attacking quartet of Goncalo Ramos, Fredrik Aursnes, Joao Mario and Rafa Silva is therefore expected to feature at Sammy Ofer Stadium.
The latter scored twice in the win over Juventus - only one fewer than in his first 26 Champions League appearances - and also in stoppage time on Saturday. However, he has yet to find the net throughout 11 away fixtures in Europe's top club competition.
Long-term absentee Felipe Morato and Germany winger Julian Draxler are both missing due to injury.
Meanwhile, Maccabi Haifa are likely to field a three-man central defence, featuring Abdoulaye Seck, who scored a brace in their 7-2 defeat to PSG; becoming only the third Senegalese player to score a Champions League double after Mamadou Niang and Sadio Mane.
Daniel Sundgren recently joined the hosts' injury list, and the Swedish defender is set to be out of action until early next year. Suf Podgoreanu, Dolev Haziza and midfielder Mahmoud Jaber are all absent too.
Maccabi Haifa possible starting lineup:
Cohen; Seck, Batubinsika, Goldberg; Atzili, Mohamed, Lavi, Abu Fani, Cornud; Chery, Pierrot
Benfica possible starting lineup:
Vlachodimos; Gilberto, Silva, Otamendi, Grimaldo; Fernandez, Luis; Mario, Rafa, Aursnes; Ramos