Saints have not conceded a goal during their last five Barclays Premier League games – the first time in 15 years they have enjoyed such a run.
That season, they kept a clean sheet in seven consecutive top-flight matches.
To match that, Saints would need to keep out both Swansea and then Chelsea at home, but Koeman says he is not worrying about records – only winning.
“Of course, if you get another clean sheet you have a high possibility to win the game, because normally we have a team who can score every game, but it's not so focused only about clean sheets. I think the focus needs to be to be prepared for the Swansea game, what we can expect and how we like to play.”
Koeman is, however, understandably delighted with his team’s current defensive form.
“I think the defensive organisation in the team is amazing, very good, and we need to keep that level, because it's always difficult to continue,” he said.
"We talk a lot about organisation in the team, that the whole team needs to have good defending, and good defending starts in front always.
“How we press, what time we press, at the right moment we try to press and that makes the team more compact and aggressive and pressing on the ball and all that kind of stuff we speak about and then it's nice to see at the weekend that it's working well.”