The Euros were meant to take place from June 12 until July 12 but will now run from June 11 to July 11 next year after UEFA stepped in and postponed the tournament in response to the coronavirus crisis.
Quique Setien was chosen to replace Ernesto Valverde as Barca manager back in January, and signed a deal set to last for two-and-a-half years.
But the new manager has suffered a difficult start to life in charge at the Nou Camp, fuelling talk that the job will be offered next to ex-player Koeman.
"The clause in my contract to go to Barça is after the Euro Cup,' Koeman told Marca.
"No date has been mentioned, so now it is after the European Championship in 2021. But anyway, I haven't thought about it for a second."
The delay to the tournament means Koeman should have injured players such as Memphis Depay available to take part.
"It is a stroke of luck, but I regret that the Eurocup is not played now. We qualified with a good level, we were in good dynamics and we wanted to continue.
"We understand the decision that has been made and we are not surprised. What is paramount is human health and preventing the spread of the coronavirus.
"Now we will consider how we can prepare for the moment when international soccer competitions are restarted."