The Blues visit St Mary's this weekend, looking to avenge Saints' 3-1 triumph at Stamford Bridge when the teams met in October.
Back then, Chelsea were under the guidance of José Mourinho, but it is now Hiddink who is at the helm, with the London club unbeaten in the nine Premier League games since he took over.
Koeman knows the abilities of Hiddink well, having played under him at PSV - winning the European Cup together in 1988 – and having previosuly worked with him as a coach with the Netherlands.
“If they change a manager it’s because they are not doing well, that’s most of the time the reason to change the manager, and you come into a new situation and you need to support and to give the players confidence and of course they had some difficult moments, injuries,” he told reporters ahead of Saturday’s game.
"[Eden] Hazard is now back on his level and [John Obi] Mikel is playing now more than he was in the beginning of the season, but the system is still the same. But I think the team is more confident and that shows why they are coming back and why they win and why it’s difficult to beat them.”
On the impact Hiddink had on him as a player and manager, Koeman said: “The biggest influence in my career as a player, but also a coach, is Johan Cruyff, but also Guus Hiddink showed me when I was a player in PSV in detail what you need to play on a high level and I had always a good understanding with him. I am looking forward to seeing him on Saturday.”