The Premier League outfit opened their European campaign with an impressive 3-0 win in Valencia on matchday one, while St Gallen were also victorious with a 2-0 victory over Kuban.
The clash at the Liberty Stadium will be the first time that the two sides have met in European competition and indeed Swansea's first meeting with Swiss opponents. St Gallen have previously met English opposition, however, when they overcame Chelsea in two legs in the fourth round of the 2000-01 UEFA Cup.
Swansea, whose spot in this competition was earned by winning the English League Cup last season, have made a fairly solid start to their Premier League campaign this season with seven points from their six matches leaving them in 13th position in the table.
Meanwhile, St Gallen have made a positive start to their domestic season with 15 points from nine matches leaving them in fourth spot in league. They are also on a 12-match unbeaten run in all competitions.
Swansea are expected to be without the services of their skipper Ashley Williams, meaning that Chico and Dwight Tiendalli will continue in defence. Neil Taylor is also expected to come into the starting XI at the expense of Welsh full-back Ben Davies.
Wilfried Bony, who has scored four times in the competition this season, will also return to the team alongside Michu, while Jose Canas and Leon Britton are expected to line up in the middle of midfield.
St Gallen: WWWDW
Possible starting lineups
Swansea: Vorm; Amat, Chico, Tiendalli, Taylor; Britton, Shelvey, Canas; Bony, Michu, Routledge
St Gallen: Lopar; Montandon, Besle, Mutsch, Martic; Kristian, Nater, Wuthrich, Mathys; Karanovic, Keita
Sports Mole says: 3-1