Michael Laudrup's side travel to Russia for their Group A encounter aware that a victory, combined with a Valencia triumph over St Gallen in Switzerland, will see them qualify for the round of 32 with two games to spare.
The two sides met in Wales a fortnight ago, when Djibril Cisse's stoppage-time penalty earned the Russian outfit a draw and their first point of the campaign after Michu looked to have extended Swansea's perfect start with a goal midway through the second half.
Cisse's strike was the first goal his side had managed in their three group fixtures, while it was the first Swansea had conceded in what has been an impressive start to their maiden Europa League campaign.
Laudrup's side won 3-0 in Valencia on matchday one, before beating St Gallen 1-0 at home in their next fixture.
Kuban, meanwhile, lost 2-0 to both opponents, leaving Viktor Goncharenko's side with much to do in the second half of the group stage if they are to have any chance of progressing.
The visitors come into the game on the back of a disappointing 1-0 Premier League defeat to fierce Welsh rivals Cardiff City on Sunday, a result that leaves them 13th in the table, three points clear of the relegation zone with just one win in their last five league outings.
Kuban, meanwhile, have reached the halfway stage of their domestic season and currently find themselves in eighth place with five wins, five draws and five defeats.
Goncharenko's side have won their last two league games however, including Sunday's 2-1 win at Krasnodar, with Gheorghe Bucur and Ivelin Popov the goalscorers.
Swansea will be boosted by the news that left-back Ben Davies is available again after recovering quicker than expected from an ankle injury, although the Wales international has stressed that the trip to Russia is not going to be an easy one.
"It's a massive game," he said. "Three points will give us a great chance to qualify. But I think Kuban proved at the Liberty (Stadium) what a good side they are and we will face another very hard game."
Davies will travel with a squad missing Michu, who limped out of Sunday's defeat in Cardiff with an ankle injury, while Garry Monk (knee) remains out, as does midfielder Pablo Hernandez (thigh).
