It would be a second successive finals for Chris Finch's men's side, but for the women it would be the first time they have qualified for the tournament, which will be staged in Poland.
It is the penultimate game of the summer for both teams, with the two squads travelling to Ukraine on Sunday, but they will want to wrap up a trip to the finals on home soil.
Finch expects a tough test when Bosnia arrive in the north west: "They're like all of the other teams in the group, they're capable of beating you if you're not ready. They've got a high basketball IQ, and have some good shooters.
They're not in a position to win the group, but they'll be fighting to get in the Additional Qualifying Round, and they're going to be dangerous."
Britain suffered their first defeat of this summer's EuroBasket qualifiers when they went down in Macedonia on Monday, and Finch is looking for a big improvement: "We need to do everything better, we need to compete better and do the little things well. We don't have a big margin for error, but we've played hard throughout and that's why we've won as many as we have. We need to get back to doing that. There's no more pressure on us on Thursday than any other game."
The men are in action at 7.30pm, and when the sides met in Sarajevo a fortnight ago, a fine shooting performance from Dan Clark helped Britain to an 84-80 victory.
The 21-year-old drained all five of his three-point efforts on the way to a 23 point haul, and with Luol Deng and Pops Mensah-Bonsu each adding 16 points, Finch's team held firm at the end of the game to take an important victory.
Bosnia arrive at the Echo Arena still looking to seal a place in next summer's additional qualifying round which sees six teams competing for the final spot in the EuroBasket finals.
Their two victories have both came at home, beating Ukraine 86-76 and Hungary 73-64, and they round off their qualifying campaign at home against Macedonia on Sunday.
American born Henry Domercant leads their scoring with 13.8 points per game, and is adding 1.8 steals.
Edin Bavcic is pulling down 5.8 rebounds per game to go with his 8.7 points, and Feliks Kojadinovic is dishing out 3.8 assists as well as hitting 4.3 points.
Before that, the women take to the floor at 4.30pm and they will look to complete a double against the Germans.
The teams met in Wolfenbüttel last week, and 20 points from Julie Page saw them gain their first EuroBasket victory of the summer with a 72-63 road win.
Jo Leedham also had a big night for Tom Maher's side with six steals to go with her 13 points and five rebounds.
Germany go into the game with a 2-2 record having split their pair of games with Ukraine - each winning on their opponents' court - and recording what could prove to be a key 63-58 win at home against Slovak Republic.
GB coach Tom Maher isn't underestimating the importance of the game: "In our collective basketball careers to say Thursday is important to us is an understatement. Britain's never qualified for the European Championship finals before and we can do so by beating Germany. Several non believers have stated that GB will never make a European Championship, we intend to prove them wrong."