Both sides secured their opening victories prior to the international break, but have had dramatic and contrasting transfer deadline-day experiences since then.
West Bromwich Albion
The win took the Baggies onto four points from as many fixtures in the opening weeks of the 2015-16 season, leaving them 15th in the table.
However, much of the talk surrounding the club in the last couple of weeks has been on the subject of Saido Berahino's future at the club. The striker has not been playing following speculation that he would move to Tottenham Hotspur, but West Brom rejected a string of bids from the London club, including one on deadline day to keep hold of the young forward.
That angered the England international though, as he took to Twitter to insist that he would not play for the club again while Jeremy Peace remains the chairman, although the PFA has moved to quash talk of a strike, while it is also being reported that Berahino will be offered a new contract.
While Berahino remains at the club, there were a couple of new arrivals late in the transfer window for the Midlands side, with defender Jonny Evans and goalkeeper Anders Lindegaard both joining from Manchester United.
West Brom could do with Berahino's goals, having scored just three times so far this season, while the addition of Evans and Lindegaard could help tighten up a defence that has conceded six times in four matches.
Recent form: WLLDLW
Recent form (all competitions): WLDLWW
The Dutchman's future at the club has been placed in doubt in recent days though, with the Netherlands national side being linked with a move for the former Holland international should they part company with Danny Blind.
Transfer deadline day saw the arrival of Virgil van Dijk at St Mary's, with the defender signing on a five-year contract from Scottish champions Celtic for a fee thought to be in the region of £11.5m.
Victor Wanyama had been expected to leave the club, having submitted a transfer request in a bid to force through a move to Tottenham Hotspur. A fee could not be agreed though, so he also remains with the club.
Graziano Pelle had struggled to impose himself up front for a couple of games, with Southampton failing to score in back-to-back matches against Everton and Watford in August, but the Italian international netted in the win over Canaries, and was on target again while away on international duty, so should be confident ahead of this match.
The Saints have not been as clinical at the back as they were during the 2014-15 season, letting in five goals so far and keeping just two clean sheets, but Koeman will be hoping that the addition of Van Dijk strengthens the back.
Recent form: WLDLDW
Recent form (all competitions): DLDDLW
Koeman has confirmed that Wanyama and Van Dijk are both in line to feature this week. Van Dijk came through 60 minutes in a behind-closed-doors friendly during the international break, while Wanyama was away with the Kenya national team after time out with a stomach bug last month.
Sadio Mane and Cuco Martina are still to arrive back at the club after international duty, but neither is thought to be carrying any knocks. However, Jordy Clasie is still sidelined with an ankle injury, while the game comes too soon for Ryan Bertrand, who is nearing full fitness after a knee problem.
Otherwise, only goalkeeper Ben Foster, who is continuing his recover from an ACL tear, is definitely out, while Berahino's availability is unclear following his comments on transfer deadline day, although he has returned to training.
Joleon Lescott started the match last time out, but has since moved to local rivals Aston Villa, while Brown Ideye, who was on the bench, has also left the club, so there will be changes for Pulis's side.
West Bromwich Albion possible starting lineup:
Lindegaard, Dawson, McAuley, Olsson, Evans, Gardner, Fletcher, Yacob, Morrison, Lambert, Rondon
Southampton possible starting lineup:
Stekelenburg, Soares, Fonte, Van Dijk, Targett, Romeu, Ward-Prowse, Wanyama, Long, Tadic, Pelle
Head To Head
When the sides met at The Hawthorns back in February, it was the home side who secured a 1-0 victory, with Berahino scoring inside the opening two minutes to secure the three points.
Southampton had been unbeaten in three appearances against the Baggies before that meeting, but have not beaten this weekend's opponents by more than one goal since 1986.
In 45 previous meetings between the two sides, there has been little to choose between them, with both claiming 14 wins, while 17 ties have ended level.
There have only ever been three red cards when Southampton have faced West Brom, and they all came in a 2013 meeting between the two at St Mary's, which saw the home side reduced to nine men and beaten 3-0, while the Baggies also finished a man short.
Hit play below to see what the Sports Mole Sofa had to say about this encounter:
We say: West Bromwich Albion 1-2 Southampton
Both sides will be confident after winning last time out, but West Brom really benefited from seeing their opponents reduced to nine men, while Southampton were cruising against Norwich before the Canaries had a player sent off. Assuming Southampton can get the ball to their attacking players, they should have enough to come away with the three points, but West Brom will likely make it difficult.