In contrast to their hosts, Gillingham will head into the first-round tie in a buoyant mood after they kicked off their League Two campaign with a dominant win over Carlisle United.
Match preview
Swansea will head into Tuesday's EFL Cup tie in a downbeat mood after their seventh consecutive Championship campaign began with a narrow 1-0 defeat to Middlesbrough.
Emmanuel Latte Lath's 25th-minute proved enough to separate the two sides, ensuring that Swansea left the Riverside Stadium with nothing to show for their efforts.
The Swans will now look to offer a positive response in their first home outing of the season, and they may be able to take confidence from the fact they have won four of their last five home games in the EFL Cup.
However, Swansea did fall to a defeat in their most recent home EFL Cup match, losing 3-2 to Bournemouth in the second round of last season's competition.
The hosts are set to face Gillingham for the first time since recording a commanding 4-1 victory in the fourth round of the FA Cup in January 2019.
Meanwhile, Gillingham boss Mark Bonner could not have wished for a better start to his tenure as he watched his side ease past Carlisle United on the opening day of the League Two season.
Timothee Dieng, Jacob Wakeling, Jack Nolan and Jonny Williams all found the net in Saturday's commanding 4-1 win at Priestfield.
After getting off to a winning start, Bonner will be hoping his side can produce another strong performance in his first away game as Gillingham boss.
The Gills may be the underdogs in Tuesday's matchup, but they can take confidence from the fact they have progressed from the first round in each of the last four seasons.
Although they could rely on penalties on Tuesday, Gillingham will enter the contest with hopes of beating Swansea for the first time since September 2006.
Swansea City form (all competitions):
L
Gillingham form (all competitions):
W
Team News
Swansea are expected to be without the services of Andy Fisher, Joe Allen, Josh Ginnelly, Sam Parker and Aimar Govea.
With Williams set to rotate his side, he could present goalkeeper Nathan Broome with the chance to make his Swansea debut.
Kyle Naughton and Kristian Pedersen could be brought into the backline, while there may also be starting opportunities for Oliver Cooper, Ronald and Zan Vipotnik.
As for Gillingham, they may be unable to call upon Elliott Nevitt, Josh Andrews and Ethan Coleman due to injury.
Midfielder Dieng will have to be assessed after he was forced off against Carlisle with a hamstring complaint.
Bonner may take the opportunity to freshen up his side, with Glenn Morris, Shadrach Ogie, Jayden Clarke and Williams all in contention to start against Swansea.
Swansea City possible starting lineup:
Vigouroux; Naughton, Darling, Cabango, Pedersen; Grimes, Fulton; Ronald, Cooper, Abdulai; Vipotnik
Gillingham possible starting lineup:
Morris; Hutton, Ogie, Ehmer, Clark; McKenzie, Little; Nolan, Williams, Clarke; Wakeling