The hosts defeated Swedish outfit Hacken in a dramatic penalty shootout to reach this stage for the first time ever, while their Norwegian counterparts recovered from a first-leg deficit to eliminate HJK Helsinki.
Match preview
History is being made for a nation with a little over 50,000 inhabitants this summer, as Tuesday's game will see the pioneering KI Klaksvik will become the first-ever Faroese side to compete in the third round of Champions League qualifying.
The 20-time national champions stunned Ferencvaros 3-0 on aggregate in round one - being held to a goalless home draw before asserting their dominance in Hungary - and shades of that result were evident when Magne Hoseth's side faced Hacken in round two.
Once again playing out a scoreless stalemate on their own territory, KI netted another three goals away from home but were matched on the attacking front by Hacken, and a 12-yard shootout would be required to separate the two sides in Gothenburg.
After Mikkel Rygaard and Simon Sandberg had fluffed their lines, veteran defender Vegard Forren held his nerve to keep the Champions League fantasy alive for KI, who are now assured of a place in the Europa Conference League group stage at worst - a feat no other team from their nation has ever achieved before.
Hoseth's men have been granted a break from their Faroe Islands Premier League title defence in order to make waves in Europe, although their domestic rivals will be playing catch-up for a while, as the reigning champions opened their campaign with 16 wins from 16 before shocking the continental landscape.
Aiming to end the KI fairytale is a Molde side who know what it takes to reach the group stages of Europe's elite tournaments, having made the Champions League, Europa League and Europa Conference League proper, while also progressing to the last-16 of the secondary competition in 2020-21.
One-time Champions League group-stage participants in the 1999-2000 season, Molde failed to make it out of their Europa Conference League section last year, and their continental adventure this time around was at risk of a premature end thanks to a 1-0 loss to HJK in their opening second-round affair.
However, Erling Moe's men turned the tie on its head last week and progressed to round three courtesy of goals from Kristian Eriksen and Ola Brynhildsen in the final 20 minutes, and as is the case with KI, Molde have also been a force to be reckoned with domestically in recent weeks.
Following an underwhelming start to their Eliteserien title defence, Molde have now won each of their last four top-flight games to rise into fourth place in the table, and they will soon compete in the semi-finals of the Norwegian Cup.
KI and Molde are not total strangers to one another, as the Norwegian side ran out 6-0 aggregate winners when the two sides clashed in the first round of qualifying for the 2003-04 UEFA Cup, so the Faroese champions have more than one incentive to keep their Champions League dream alive here.
KI Klaksvik Champions League form:
D
W
D
W
KI Klaksvik form (all competitions):
Molde Champions League form:
L
W
Molde form (all competitions):
Team News
While KI came through their enthralling penalty-shootout win over Hacken with no new injures to worry about, 14-goal top scorer Pall Klettskard has not played a single minute in the qualifying competition so far, having been plagued by an unspecified issue.
Klettskard's lengthy absence only makes the hosts' feats all the more remarkable, but the 33-year-old was back on the bench for the second leg of their tie with Hacken and may now be considered for a run-out on Tuesday, although his lack of match fitness could restrict him to a cameo role.
Instead, Luc Kassi will expect to hold his place at the tip of the attack, while second-round hero Forren - once of Southampton and Brighton & Hove Albion - will line up against the club he previously made 369 appearances for.
Similarly, Molde also came out of their second-leg win over HJK unscathed, but Moe is facing quite the dilemma in the centre of the field after Eriksen's crucial contribution to that success.
The 28-year-old had only been on the field for 15 minutes as a substitute before opening the scoring last Wednesday, but neither Markus Andre Kaasa nor captain Magnus Wolff Eikrem will feel that their places are in any real danger.
KI Klaksvik possible starting lineup:
Johansson; Petersen, Faero, Forren; Danielsen, Andreasen, Pavlovic, Joensen; Frederiskberg, Kassi, Kronberg
Molde possible starting lineup:
Karlstrom; Haugan, Bjornbak, Hagelskjaer; Linnes, Eriksen, Mannsverk, Kaasa, Haugen; Eikrem, Brynhildsen
We say: KI Klaksvik 0-2 Molde
While KI have not found the formula for attacking success at home in the Champions League thus far, they have more than made up for it with rearguard resilience before packing their best shooting boots for the second leg.
Molde may therefore need to have their wits about them at the Aker Stadion next week - especially with Klettskard returning to full fitness - but they should still put a dent in KI's European aspirations with a couple of goals in Torshavn.