Ernesto Valverde finds himself under pressure at the Nou Camp despite the fact that Barcelona are top of La Liga.
But the Blaugrana have been beaten three times in the league already this season and lost again on Saturday, 3-1 to Levante.
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The Spanish press are reporting that Koeman is the preferred candidate among the players to replace Valverde and after Koeman's superior Nico-Jan Hoogma revealed a release clause in his contract, the former Everton boss felt he had to clarify the situation publicly.
“[The clause] only about Barcelona and only about a moment after the European Championships," Koeman said.
"I am not leaving now, that is one hundred percent certain."
Koeman spent six years as a player at Barcelona, winning four league titles and a European Cup, scoring an extra-time winner against Sampdoria in the final to write his name into club folklore.
The 56-year-old rejoined Barcelona in 1998 as an assistant coach but has never done the top job despite an extensive managerial CV.
However, he has admitted that the pull of Barca could be too great if they were to come calling after the Euros.
Koeman added: “After the European Championships there is an evaluation moment, who knows, the KNVB [Dutch football's governing body] will perhaps say 'we have performed so badly at the European Championships, we are not going any further' but I have the opportunity to leave for one club. And there’s only one club in it.
“And I can safely say that I am not leaving for anyone else as the national coach of the Dutch national team.”
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