The Dutchman, who impressed in the Netherlands with Feyenoord, arrived as Mauricio Pochettino's replacement this summer, and has guided the Saints to eight wins from the first 11 games.
New signings such as Fraser Forster, Toby Alderweireld, Ryan Bertrand, Dusan Tadic, Sadio Mane and Graziano Pelle have impressed so far this term, making fans completely forget about the mass exit from St. Mary's Stadium this summer.
With the Saints sitting just four points off leaders Chelsea after a quarter of the season, fans are starting to dream of a push for Champions League football - and at their current pace, they'll be in the picture.
The biggest factor in Southampton's great start has been conceding just five goals in 11 games, but the agent of Aston Villa centre back Ron Vlaar admitted that there is interest from the Saints.
"Last summer, Southampton were interested in Ron," revealed Arnold Oosterveer. "But we asked ourselves whether that club would be a step forward compared to Aston Villa. Now that club are suddenly second, so things can happen quickly."
Vlaar was a key player under Koeman at Feyenoord, and his impressive displays for the Netherlands at the World Cup and with Aston Villa this season has led to interest from Arsenal and Manchester United too.
However, if the Saints have genuine aspirations of a top four finish, they may yet want to add Vlaar to make their defence even sterner, particularly with speculation that Atletico Madrid want to take Alderweireld back from his loan spell.
Vlaar is more likely to play first team football at Southampton than he is at Arsenal or Manchester United, and a reunion with Koeman could be very appealing.
It's ambitious to try and beat two of the biggest clubs in England to the signing of a top defender, but that's where Southampton are in their progress right now.
They're a club on the up, a club heading in the right direction, and they can prove that they are ready to mix it with the big boys by challenging Arsenal and Manchester United for the signature of Vlaar.