The Polish side defeated Aris Limassol in the third qualifying round, while Copenhagen were victorious on penalties against Sparta Prague.
Match preview
Rakow have never made it to the Champions League group phase, but their impressive run in the qualifying stages has caught the eye.
The Polish champions have played six times across three qualifying rounds, claiming five victories and playing out one draw.
Dawid Szwarga's troops defeated Flora in the first round in qualifying before seeing off the threat of Qarabag (4-3 on aggregate) and Aris in the second and third rounds respectively.
Their unbeaten run is put to another test on Tuesday, when they play host to their Danish opponents, looking to secure a positive result that puts them in an encouraging position for the reverse fixture on August 30.
Rakow have claimed three wins from three in their home games in all three qualifying rounds, thus giving the hosts the much-needed confidence before Tuesday's fixture.
For their part, Copenhagen are favourites to make the Champions League group stage, but they must cope with being the fancied side to advance.
The Danish club have played the last two rounds to get within a couple of games to be one of the 32 teams involved in this year's competition.
Jacob Neestrup's side needed penalties to overcome Sparta Prague in the previous tie, a topsy-turvy game that saw the Lions lead 1-0 in the second leg, turn the game around to move 2-1 up before falling behind 3-2.
A Viktor Claesson 112th-minute equaliser made it 3-3 on the night and aggregate, taking the tie into penalties.
It remains to be seen if Copenhagen's superior history in these situations gives them the edge over Rakow, whose extraordinary run has been incredible.
Rakow Czestochowa Champions League form:
W
W
W
D
W
W
Rakow Czestochowa form (all competitions):
D
D
W
L
W
W
Copenhagen Champions League form:
W
W
D
W
Copenhagen form (all competitions):
W
W
D
W
W
W
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Team News
Fabian Piasecki did not start in Rakow's game at the weekend, but the striker — who has netted twice in previous rounds — should replace Lukasz Zwolinski in the team.
Giannis Papanikolaou was in fine form in Saturday's win over Stal Mielec, opening the scoring just before the interlude, and the midfield man is expected to start on Tuesday.
Rakow are expected to line up in a 3-4-3, with Szwarga not anticipated to change his approach.
Denis Vavro went off before the hour in Copenhagen's triumph over Sparta Prague, missing out on the 2-0 win at Hvidovre on Friday, thus making him doubtful for Tuesday.
Mohamed Elyounoussi came off the bench to score in the league over the weekend, and the former Southampton man could return to the XI against Rakow.
Kamil Grabara made 10 saves in the 3-3 draw with Sparta Prague, making him a potential match-winner in the tie.
Rakow Czestochowa possible starting lineup:
Kovacevic; Racovitan, Arsenic, Rundic; Tudor, Papanikolaou, Lederman, Carlos; Drachal, Piasecki, Cebula
Copenhagen possible starting lineup:
Grabara; Jelert, Diks, Lund, Sorensen; Goncalves, Jensen, Lerager; Elyounoussi, Larsson, Achouri
We say: Rakow Czestochowa 2-1 Copenhagen
Rakow's fairy-tale run should see them claim another Champions League victory, with Copenhagen unlikely to stop the Polish side's unbeaten streak on Tuesday.