Koeman has worked wonders on the South Coast since joining from Feyenoord in 2014, and continues to push forward despite losing a host of key players.
The Dutchman has watched on as the likes of Nathaniel Clyne, Calum Chambers, Dejan Lovren, Toby Aldereweireld, Luke Shaw, Morgan Schneiderlin, Adam Lallana and Rickie Lambert all left St. Mary's Stadium in order to join Premier League rivals.
Signings such as Fraser Forster, Ryan Bertrand, Sadio Mane and Graziano Pelle have helped the Saints recover from those losses, and Koeman has played down any talk of him following those previous names in leaving the club, as quoted by the Daily Mirror.
"Be happy as I am now," said Koeman. "And that means to work with a great club, with good people to develop the team and still to have the belief between the technical staff and players, to go on. That's the key word, to continue or not, but it's my second season. We have time to think about it."
Koeman also spoke about his ambitions for the club, and admitted that he wants to win some silverware - and noted that he would love Southampton to copy what Aston Villa did last season by reaching the FA Cup final.
"The ambition is to continue and to improve. Make it better in how we play and get results and to achieve what we did last year and the ambition to win a title. It is very difficult, we know, but if Aston Villa can play in the FA Cup final, why not Southampton? That would be great and we will fight for that," he added.
Villa may have been thrashed 4-0 by Arsenal in that final, but it seems that their run to Wembley last season has inspired Koeman to target the same for Southampton this term - and given the players at his disposal, it's far from an unrealistic target for the Saints.