After beating Italian giants Juventus last year, Haifa have ambitions of being one of the of 32 teams to battle it out again this autumn; and after taking in a four-goal lead in last week's first leg, they already have one foot in the second qualifying round.
Match preview
In a quartet also featuring established European heavyweights Paris Saint-Germain and Benfica, last season Maccabi Haifa experienced mixed fortunes in Champions League Group H: being thumped 7-2 and 6-1 just weeks after writing themselves into history by toppling Juventus.
While their 2-0 win over an ailing Old Lady on the fourth matchday will never be forgotten by fans - and they only missed out on a Europa League playoff place on goal difference - Messay Dego's current side must negotiate four rounds of qualifying before having the chance to repeat such feats on the grand stage.
Last Tuesday, the Greens got their quest off to a near-perfect start as they swept aside Champions League newcomers Hamrun Spartans at Centenary Stadium - Haitian striker Frantzdy Pierrot scoring twice in a comprehensive 4-0 victory.
Since securing a third successive Israeli Premier League title last season, Dego has stepped into the breach following Barak Bakhar's switch to Red Star of Serbia, and ahead of a Super Cup clash with Beitar Jerusalem on Saturday he will want to finish off the job without any fuss.
Starting with a surely unassailable advantage and benefiting from the second leg being held on home soil, Haifa will already have an eye on the second round, where either Farul Constanta or Sheriff Tiraspol will await.
While their hosts are bound for a place in round two, should Hamrun Spartans fail to pull off an implausible comeback, a spot in the Europa Conference League second qualifying round will serve as their consolation prize.
Representing Malta in the top tier of European football for the first time since 1991 - when Benfica handed them a 10-0 hammering across two legs in the European Cup first round - Hamrun may be set to bow out once again.
Tas-Sikkina cruised to the Maltese Premier League title last term, racking up 69 points and conceding just 10 goals in the process, as they finished 19 points clear of runners-up Birkirkara to be crowned national champions for a ninth time.
After crowd trouble during the first leg in Ta'Qali, Hamrun have seen UEFA turn down a request to stage this week's return at a neutral venue, amid stated concern for the safety of their travelling contingent.
Head coach Luciano Zauri - a former Italy international, who took the reins in April - will seek to block out such noise ahead of Tuesday's contest, in which a minor miracle is required to overturn his side's sizeable deficit.
Maccabi Haifa Champions League form:
W
Hamrun Spartans Champions League form:
L
Team News
With an important game on the horizon at the weekend and progress to the second round all but assured, Maccabi Haifa could make several changes to their starting XI on Tuesday evening.
Centre-back Sean Goldberg, captain Tjaronn Chery and forward Frantzdy Pierrot provided the spine of last week's team, but the likes of Suf Podgoreanu and 37-year-old playmaker Lior Refaelov - the latter of whom recently returned to the Greens from Belgium - could be among those promoted from the bench.
After being consigned to a substitute role in Malta, midfielder Mahmoud Jaber - an Israeli international whose brother plays for Palestine - is another potential starter at Sammy Ofer Stadium.
Meanwhile, Hamrun have no such squad depth to call upon, so 40-year-old ex-Italy goalkeeper Federico Marchetti should start behind a largely unchanged lineup, with Steve Borg skippering the side from the centre of a back three.
Recent signing Uros Djuranovic made his competitive debut for the club in the first leg, and the Montenegrin striker is set to be retained up front, flanked by Brazilian duo Jonny and Elionay.
Maccabi Haifa possible starting lineup:
Nitzan; Sundgren, Seck, Goldberg; Sabia, Jaber, Chery, Cornud; Refaelov; Podgoreanu, David
Hamrun Spartans possible starting lineup:
Marchetti; Camenzuli, Borg, Bilic; Corbalan, Emerson, Bjelicic, Prsa; Elionay, Djuranovic, Jonny