The sides sit third and fourth in the table respectively, having enjoyed fine starts to the campaign.
Swansea have won three of the opening four games, suffering their first defeat on Saturday at the hands of top-of-the-table Chelsea.
And manager Garry Monk is hoping they can immediately bounce back from that 4-2 loss at Stamford Bridge.
He said: "Initially, I was disappointed but there were plenty of positive in the way we played [against Chelsea].
"In the second half, there were things to work on and prolong the things we did well in first half.
"Chelsea overpowered us second half. We have spoken a lot about us this week and we have always had the mentality that we never give up and we go right to the end."
Southampton's early-season form has been even more impressive given the question marks surrounding them when Ronald Koeman replaced Mauricio Pochettino as manager.
Luke Shaw, Adam Lallana, Rickie Lambert and Dejan Lovren were high-profile departures, but a new-look side built by Koeman have lifted the gloom at St Mary's.
Southampton eased to a comprehensive 4-0 victory over Newcastle last weekend, leading to further optimism at the south-coast club.
Their exploits early in the season have caught the eye of Monk, who spent eight years at Southampton earlier in his career.
He said: “I think they have recovered from losing players and used the money to buy some quality players.
"They have played well in their last two games and are scoring fantastic goals.
"Their style has tweaked but they are similar to ourselves in way they set up; the wingers play a bit inside and float about more.
"I still look out for Southampton results; my time there was brilliant and I have a lot of affection for the club and friends there."
The admiration between the sides is mutual, with Koeman waxing lyrical about Swansea.
Koeman said: "It’s nice to see how they play because it’s similar to what we like to do and how we like to play.
"They’re a team who press very well in midfield and a team who like to dominate their opponents and it’s similar to what we like to do and I think that will be very interesting for Saturday."
Koeman also confirmed that Shane Long should be fit, having taken a blow to the head against Newcastle. However, Sadio Mane is not expected to feature despite the midfielder's work permit being approved.
Swansea, meanwhile, have been dealt a blow with the news Jordi Amat will be sidelined for six weeks.
Southampton enjoyed dominance in these fixtures last season, winning 2-0 at St Mary's before leaving the Liberty Stadium with a 1-0 triumph.
