These are the only two clubs yet to pick up a point in the Premier League so far this season, with hosts Everton making their worst start to a campaign for 66 years.
Match preview
It was a case of deja vu on Saturday for Everton, as the Toffees squandered a two-goal lead for the second game in succession.
Sean Dyche's side stunned Aston Villa by taking a 2-0 lead inside 30 minutes at Villa Park, with Dwight McNeil and Dominic Calvert-Lewin both beating Emiliano Martinez in the home goal.
However, an instant reply by Ollie Watkins changed the whole feel of the game, as Everton began to look vulnerable once again, and the England international scored again to level proceedings early in the second half, before Jhon Duran's stunning strike sealed the 3-2 win for Villa.
It was not quite as catastrophic as their previous defeat at home to Bournemouth, when Everton led with three minutes of normal time remaining and went on to lose, but a soft underbelly is rearing its head in the ranks.
Dyche has come in for questioning considering his whole game plan is often centred around keeping it tight, nicking a goal or two, and then holding on to what you have, as Everton have now lost 23 points from winning positions since the start of last season.
Not since 1958 have Everton lost their first four league games of a season, meaning their trip to Leicester City next weekend is now absolutely huge in regards to Dyche's future, and that could take priority over this cup tie.
Starved of silverware though, Everton fans will not accept passing up on a relatively good opportunity to reach the fourth round of a competition they have never won.
The Toffees have not tasted success since 1995, with only one final to show for themselves in the period since.
Last season could well have been a golden opportunity to end that run, but after Amadou Onana missed a potential game-winning penalty in their EFL Cup quarter-final tie with Fulham, Everton were floored, and then did not win again for almost four months.
Penalties also decided the last cup meeting between these two sides, which also came at Goodison back in 2018, and once more Everton came up short, as Southampton progressed.
Southampton's last visit to the blue half of Merseyside also ended in victory, as a James Ward-Prowse double saw them win 2-1 in January 2023, but they still went on to suffer relegation that season.
The visitors travel to Goodison once again as relegation candidates, but they can solely focus on cup matters for a few days at least after a fourth straight loss of their own Saturday against Manchester United.
Like Everton, Southampton also made a bright start, but they could not take advantage, as Cameron Archer missed a first-half penalty which would have given them the lead.
In the ultimate sucker punch, Man United went up the other end and scored twice before the interval, and then went on to win 3-0 at St Mary's.
Manager Russell Martin is under slightly less pressure than Dyche, given the respective pre-season ambitions, but his progressive style of play has come under fire for being ineffective so far.
Toothlessness in attack has been most costly though, as their only goal this season remains a late consolation against Brentford in a 3-1 defeat, and failing to score against 10-man Newcastle United, and missing a penalty at the weekend sums up the current state they find themselves in.
The EFL Cup has often been a happy hunting ground for the Saints though, as they have reached round four in 10 of the last 13 seasons, as well as reaching the final in 2017 and the semi-finals in 2023.
Everton EFL Cup form:
W
Everton form (all competitions):
Southampton EFL Cup form:
W
Southampton form (all competitions):
Team News
As has often been the case during Dyche's tenure, he will prioritise league over cup, and Everton's current position at the bottom of the standings may lead to many personnel changes.
New signings Jesper Lindstrom and Jake O'Brien could start to provide a further opportunity for them to settle into the side as they did in the last round against Doncaster Rovers.
Jarrad Branthwaite is most likely going to be held back for the weekend trip to the King Power Stadium after missing the first month of the season, and so could Vitalii Mykolenko if he does not recover from illness in time.
James Garner and Abdoulaye Doucoure have lost their places in the league XI at the moment but could feature from the start, while Beto may also replace Calvert-Lewin up front.
Jack Stephens will be banned for Southampton after he was sent off for a rash challenge on Alejandro Garnacho at the weekend.
Teenager Tyler Dibling was fantastic on his full Premier League debut, winning the penalty which Archer ultimately missed, so he could drop out to be kept fresh for the weekend.
Martin changed the entire team for their trip to Cardiff City in the last round, and with Premier League points a must, he may do something similar here.
On the injury front, Kamaldeen Sulemana and goalkeeper Gavin Bazunu remain out, while Will Smallbone is unlikely to feature.
Everton possible starting lineup:
Pickford, Garner, Tarkowski, O'Brien, Young; Lindstrom, Iroegbunam, Doucoure, McNeil; Ndiaye, Beto
Southampton possible starting lineup:
McCarthy; Bree, Harwood-Bellis, Edwards, Taylor; Aribo, Lallana, Mateus Fernandes; Fraser, Armstrong, Amo-Ameyaw
We say: Everton 1-1 Southampton (Southampton win on pens)
Nothing seems to be going right for Everton, even when things look like they are improving, as their two recent collapses show, and another defeat here will be hugely demoralising for the home support.