The former Feyenoord manager has been championed in the Dutch media as an option to replace Guus Hiddink, but Koeman only has eyes for St Mary's.
The Netherlands have disappointed since returning from what was a successful World Cup in Brazil. Louis van Gaal guided them to a third-placed finish in the summer before taking over at Manchester United, with his replacement Guus Hiddink returning for a second spell in charge of the national team as his replacement.
But three defeats in four games has led to questions being asked of the former Chelsea boss despite his limited time in charge.
Ronald de Boer, former Netherlands player and brother of Ajax boss Frank de Boer, had said earlier in the week after seeing the Netherlands lose to Iceland that Hiddink was an outdated coach and that one of the younger managers in the Dutch game should be given a chance as manager of the national team, before name checking former Feyenoord boss Koeman.
The Barcelona legend only took over at St Mary's this summer, replacing Mauricio Pochettino, and has made a stunning start to Premier League life by guiding the South Coast club to the Premier League top three despite massive squad upheaval.
"He said the same thing last season when the Federation chose Hiddink," said Koeman of De Boer's show of public support.
"He said that this team needs a younger coach, a coach from a new generation.
"I am the manager of Southampton, I am not the national manager and I will not be the next national manager.
"We are not happy about the performance of Holland. After this bad start for the Europeans, it will be difficult. Of course, I would prefer if Holland would win as I'm Dutch."