The Dutchman, who spent six years at the Camp Nou as a player from 1989 to 1995, insisted, however, he would honour his contract with the Toffees.
"Everyone knows I'm Barca, they know my love for the club where I grew up as a player and as a person," Koeman said.
"In my life as a professional coach, I have two dreams to fulfil. One, to coach my national team, Holland. I could have done it but my obligation to Everton prevented me.
"My other wish, my other dream, is to one day coach Barca. That's the truth."
The former Barca defender has been linked with a return to Catalonia since it was announced Luis Enrique will leave the Blaugrana at the end of the season.
But Koeman told the BBC: "I don't see me being the next manager. I mentioned several times it's human ambition - for players, for managers.
"That doesn't change my position or contract with Everton. I'm really happy, I'm looking forward to next season."