The Swans exited the competition at this stage last season when trying to defend their title and will be hoping for another deep run this term.
After beginning the season with three straight victories, Garry Monk's side have lost their last two games to fall to fifth in the table. They reached this stage by edging out Championship Rotherham United last month.
Monk is likely to make a number of other changes to rest key players.
Everton, meanwhile, are entering the competition at the third-round stage as they are in Europe this season. Roberto Martinez's side will have had just two days' rest as they played Crystal Palace on Sunday, going down 3-2 at home to the Eagles.
Like Monk, Martinez is set to shake up his starting XI and will have two long-term absentees available again for selection.
This will be the first League Cup meeting between the two sides. Everton have never lost to Swansea before, winning 15 and drawing five in all previous meetings.
Possible starting lineups
Swansea: Tremmel; Tiendalli, Bartley, Williams, Richards; Routledge, Ki, Carroll, Montero; Emnes, Gomis
Everton: Robles; Hibbert, Stones, Alcaraz, Oviedo; Besic, Osman, Gibson; McGeady, Eto'o, Atsu
Sports Mole says: 2-2