The 56-year-old spent six years at Barca as a player before later having a spell as Louis van Gaal's assistant from 1998 to 2000 and he has been strongly linked with a return since overseeing an impressive improvement of the Netherlands national team.
Koeman took over the Oranje last year after they had missed out on a spot at the 2018 World Cup, but he has since transformed them into a force, leading the team to the Nations League final and on course to qualify for Euro 2020.
It was recently confirmed Koeman has a clause in his contract that would allow him to leave Netherlands for Camp Nou if the situation arose after the Euros, and with Ernesto Valverde under increasing pressure it looks likely a change could be made in the next year.
Koeman insists he would not turn his back on Netherlands before Euro 2020, however.
"Joining [Barcelona] is a possibility," Koeman told reporters. "But only after Euro 2020.
"I don't know if I'll keep [speaking about the Barca job] in the future because it's a bit strange to speak about the possibility of going to the club while you're the Netherlands coach.
"There is no other side I would leave Netherlands for except for Barcelona."
Netherlands have two Euro 2020 qualifiers remaining against Northern Ireland and Estonia. They head into the double-header level on 15 points with Germany in Group C, but ahead of them by virtue of a better head-to-head record.