After weekend defeats, the two nations both trail Denmark and Slovenia by four points, so even a win in Helsinki may not be enough to keep them in contention.
Match preview
As the top four teams in European Championship qualifying Group H were separated by just one point heading into this month's fixtures, there was plenty riding on Finland's game against Slovenia on Saturday.
Markku Kanerva's men could not cope with the cool finishing of Slovenian starlet Benjamin Sesko, however, and the young forward's first-half brace effectively sunk Finnish hopes in a 3-0 defeat at Ljubljana's Stadion Stozice.
As a result, the Finns would be unable to finish inside the top two should they lose to Kazakhstan on Tuesday and both Denmark and Slovenia win, which would leave them relying on a potential back-door route to next summer's finals.
While Finland - who play Northern Ireland and San Marino in November - are now four points behind Group H's leading pair, at least one of Denmark and Slovenia will drop points when they meet next month, so the flame of hope still flickers.
Even if they fail to pull off such a comeback, the Eagle-Owls may still be handed a playoff place based on their efforts in League B of the most recent UEFA Nations League, so all would not be lost.
Successive defeats without scoring a goal may have dented Finland's confidence a little, but the Nordic nation are still very much in the mix for a second finals appearance, having been knocked out at the group stage of Euro 2020.
By contrast with Tuesday's hosts, Kazakhstan have never participated in a major tournament at senior level, so qualification for Germany 2024 would break new ground for the former Soviet state.
A three-game winning run earlier this year - featuring victories over Denmark, Northern Ireland and San Marino - took Magomed Adiyev's men into contention, but having lost 1-0 to Finland in last month's reverse fixture before beating Northern Ireland again, they were defeated for the second time in three qualifiers at the weekend.
Denmark gained revenge for their loss in Astana with a 3-1 home win over Kazakhstan, in which substitute Yan Vorogovskiy's second-half strike proved only a consolation for the visitors, who had gone three goals down shortly after the break.
Therefore, the Kazakhs will be unable to finish in the top two if they lose at Helsinki's Olympic Stadium and both Denmark and Slovenia win, but - like their opponents - a playoff place provides them with another chance.
Due to their results in League C of the Nations League, Kazakhstan would be confirmed in the playoffs if they cannot qualify automatically, so the pressure is off to some extent.
Having lost all five of their previous competitive meetings with Finland, scoring just one goal in the process, that may just as well for FIFA's 100th-ranked nation.
Finland Euro Champ Qualifying form:
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Kazakhstan Euro Champ Qualifying form:
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Team News
Scorer of the winning goal in September's away win over Kazakhstan, Nordsjaelland midfielder Oliver Antman is Finland's most notable injury absentee this month.
With Antman out of action, Benjamin Kallman and Glen Kamara provided support to 38-goal striker Teemu Pukki on Saturday, but after the Finns failed to score for a second successive qualifier, coach Markku Kanerva may bring in Joel Pohjanpalo to freshen up his front line.
Winger Daniel Hakans, who is the hosts' top scorer in Euro 2024 qualifying thanks to a hat-trick against San Marino, can also be hopeful of being promoted to the starting XI.
Meanwhile, Kazakhstan will arrive in Helsinki with no less than five players one booking away from suspension, including Maksim Samorodov, who has scored twice in seven Group H games so far.
Head coach Magomed Adiyev knows that hopes of automatic qualification ride on Tuesday's result, so is unlikely to make many changes on that basis: matches against San Marino and Slovenia next month could be dead-rubbers in any case.
Therefore, Samorodov should support Astana striker Abat Aymbetov in attack, with Zenit St Petersburg's Nuraly Alip helming a three-man defence.
Finland possible starting lineup:
Hradecky; Hoskonen, Ivanov, Vaisanen; Alho, Schuller, Kamara, Uronen; Kallmann, Pukki, Pohjanpalo
Kazakhstan possible starting lineup:
Shatskiy; Bystrov, Alip, Marochkin; Kairov, Zaynutdinov, Kuat, Dosmagambetov; Orazov, Aymbetov, Samorodov