The 56-year-old has been tipped to succeed under-fire Barca boss Ernesto Valverde , whose future has been called into question following the Spanish giants' disappointing end to the season.
A 4-0 second-leg loss to Liverpool ended Barcelona's Champions League hopes at the semi-final stage as they crashed out 4-3 on aggregate, and they suffered a surprise 2-1 defeat to Valencia in last weekend's Copa del Rey final.
However, despite reports in the Spanish press that Koeman is being considered as a possible replacement for Valverde, the former Barca defender was unwilling to comment on matters beyond Netherlands' Nations League preparations.
"I think this is about the Dutch national team, so I would like to leave it at that," he said at Tuesday's news conference.
Asked if he was willing to give assurances that he will stay on as Oranje head coach, Koeman responded: "That would be very easy, but I will not."
Koeman is preparing his side for the inaugural Nations League finals, with the Dutch taking on England in the semi-finals on June 6 – the day after hosts Portugal face Switzerland in the other last-four game.
Despite a gruelling campaign for the Ajax contingent in his squad, Koeman insists the Eredivisie winners' run to the semi-finals of the Champions League can only be considered a positive.
"It was great to watch the development of Ajax players this season," he said. "The success in Europe hasn't proved to be prohibitive for development. Many players have grown as a result.
"But by looking at how the guys have trained, you wouldn't have the idea that they're thinking that the season's over already. I don't see that they're struggling with a few more matches, or that they're tired."
Unlike the other three sides left in the competition, the Dutch players had an extended break heading into the 2018-19 campaign after they failed to qualify for the World Cup in Russia.
Koeman was appointed following that failed qualification campaign, replacing former Sunderland boss Dick Advocaat.