The Saints started their Championship campaign with a 2-1 victory over Sheffield Wednesday on Friday, while Gillingham beat Stockport County 1-0 in their League Two opener on Saturday.
Match preview
Gillingham managed to survive in League Two last season, ultimately finishing 17th in the table, some 12 points above the relegation zone, and head coach Neil Harris will now be looking to push his side towards the top half of the division in 2023-24.
The Gills made the perfect start to their League Two campaign on Saturday, recording a 1-0 victory over Stockport, with Robbie McKenzie winning it in the 86th minute of the contest.
Gillingham have never won the League Cup, and in truth, the competition will not mean too much for the club this term, with almost all of their focus being on the league.
Harris's side will host Accrington Stanley in League Two next weekend, while they will also take on Sutton United, Crawley Town and Colchester United before the end of the month.
Gillingham actually beat Southampton 2-1 when the two teams last locked horns in League One back in May 2010, but it would be fair to say that a lot has changed at both clubs since then.
Southampton, as mentioned, made the perfect start to life back in the Championship, recording a 2-1 victory over Sheffield Wednesday on Friday evening, with Che Adams netting the winner late on.
Russell Martin's side have thus far managed to keep hold of their captain James Ward-Prowse, but there remains speculation surrounding the futures of the likes of Romeo Lavia and Adams, and there is expected to be more movement both in and out before the transfer window closes.
The Saints have only actually made two signings this summer, bringing in Shea Charles and Ryan Manning, while their biggest departure at this stage has been Mohammed Salisu to Monaco.
With the current squad, Southampton will fancy their chances of making a strong push for a return to the Premier League, although it is arguably one of the strongest divisions in recent memory this term.
The Saints have never won the League Cup, but they have progressed to the final on two separate occasions, including in 2017, when they were beaten 3-2 by Manchester United.
Gillingham form (all competitions):
Southampton form (all competitions):
Team News
Gillingham head coach Evans will shuffle his pack on Tuesday, as he will want to keep his key players fresh for the league contest with Accrington next weekend.
McKenzie came off the bench to score the winner against Stockport and could potentially be introduced for a start on Tuesday, while Ashley Nadesan and Max Clark should also come into the XI.
Evans is likely to change his goalkeeper, meanwhile, with 39-year-old Glenn Morris in line for a start here.
As for Southampton, Valentino Livramento was not involved on Friday, with the defender believed to be closing in on a move to Newcastle United.
Lavia was also an unused substitute amid the speculation surrounding a switch to Liverpool, and the midfielder is not expected to feature in this contest.
Adams is also being linked with a departure but should come into the XI here, while Stuart Armstrong, Joe Aribo, Alex McCarthy, Charles, Lyanco and Moussa Djenepo are also expected to be introduced into the side.
Ward-Prowse played the full 90 minutes against the Owls last time out, but the captain is likely to be given a rest in the EFL Cup first-round contest at Gillingham.
Gillingham possible starting lineup:
Morris; McKenzie, Ehmer, Ogie, Clark; Clarke, Chambers; Nadesan, Gbode, J Williams; Nichols
Southampton possible starting lineup:
McCarthy; Walker-Peters, Stephens, Lyanco, Manning; S Armstrong, Aribo, Smallbone, Charles; Djenepo, Adams
We say: Gillingham 0-2 Southampton
Southampton's strength in depth is very impressive, and head coach Martin will still be able to name a strong XI even if he makes wholesale changes from the clash with Sheffield Wednesday. Gillingham boss Evans will also rest some important players, so we are expecting this to be a comfortable game for the visitors.