The campaign may still be in its infancy but those predicting a season of woe at St Mary's could not be further off the mark judging by early displays.
Saints enter this weekend's match with QPR second in the Barclays Premier League and looking for a sixth successive win in all competitions.
The latest victory saw them return from Arsenal on Tuesday as 2-1 victors in the Capital One Cup - a performance and result that saw Koeman give his players Wednesday off.
There is nothing unusual about that, although the fact his squad instead asked to come to training is something he has not experienced in any of his previous managerial roles at clubs like Ajax, Benfica and Valencia.
"The players showed a great ambition because we planned last Wednesday as a day off after the Tuesday and Jose Fonte said to me: 'Boss, we would like to come to train tomorrow'," he said.
"I said 'But you have a day off - I've planned a lot of things with my wife!' But we changed it and we had a recovering session.
"I never had that - a team, a squad say 'no day off' and that means a lot for me, that means a lot about the ambition of the players.
"We spoke to each other and said: 'Okay, if you win against Queens Park then you get that day off for next week', and we hope to win on Saturday."
Such attitude and togetherness has impressed Koeman, who himself was one of the world's best players in his day.
The former defender was key to Barcelona's European Cup triumph in 1992 and knows reaching that competition with Saints is beyond them this term, despite their fine start.
"It isn't realistic" he said of a top-four finish
"I remember one of the questions in the last week of starting the season and that question was totally different and that's football.
"But you can't say anything about that because we've played only five games in the Premier League and at the end of the season are 38.
"We know it's a long season, it's a tough season.
"Okay, we know we have a very good start of the season, with all the changes we make from the beginning and, of course, after the win of last Tuesday the expectations of the fans, of the press is much higher than it was before the first game.
"But it will be more difficult and we have to realise that and to keep going with what we did until today."
Few expect Southampton to come off the rails against a QPR side whose away league matches this season have both ended in 4-0 defeats.
A similar result would be particularly sweet for many Saints fans given the west Londoners are managed by Harry Redknapp.
In 2005, the 67-year-old was in charge as Saints dropped out of the top-flight for the first time in 27 years before rejoining bitter rivals Portsmouth just months later - something Koeman was completely unaware of.
"He is not [a popular figure]? Why? I didn't know that," he said.
"What I see now in the Premier League, even in the away games, is a lot of respect of the crowd and that's much different than we have in Holland.
"I think Harry Redknapp is a name, it's a successful manager and a lot of experience, but I'm not the person to look to the history of the managers and the players.
"In my opinion, he's a manager who I respect and I think everybody has to respect."
Source : PA
Source: PA