Koeman was placed in charge at St Mary's at the start of the 2014/15 campaign and has enjoyed great success, guiding the club into the Europa League last season.
His style has brought the very best out of the Saints' squad, even though the Dutch boss has had to contend with losing some of his more talented players in summer transfer windows.
And Davis has said of the 52-year-old: "He’s been great since he came. All the players would tell you that.
"He’s very level-headed, he doesn’t get too up or down and I think that’s a good approach to have because you know in football things start changing quite quickly.
“One week to the next it can be a different mentality but the manager’s very levelled headed and has been great since he came in.”
It was expected that Koeman's job at Southampton may have been a difficult one, as he took over from Mauricio Pochettino, who had been very successful.
But, he has actually improved the team and the south coast club are now firmly established as a Premier League outfit, only five years after they were playing in League One.
It has been a rapid rise for the Saints, and there is plenty of cause for optimism for supporters of the club.
Despite a slow start to the current campaign, Koeman's side seem to have settled into their quest, and they are now in 10th place in the Premier League table, having picked up an impressive 3-1 victory over Swansea City in their most recent outing.