The Dutchman, a former player at the Nou Camp, has been linked with a return to Spain at the end of the season following Luis Enrique’s announcement that he will step down as manager in the summer.
Koeman, who has another two years to run on his current contract at Goodison Park, has previously dismissed speculation of a move.
But while admitting his ambitions to one day return to Catalonia he also knows there’s work to be done on Merseyside first.
"Everyone knows that I am from Barca, they know my love for a club where I grew up as a player and as a person," he told Spanish newspaper Sport.
"In football, as in life, as in business, everything can be talked about and discussed.
"In my life as a professional coach I have two dreams to fulfil. One, coach the selection of my country, Holland (he was previously assistant to Guus Hiddink for the 1998 World Cup)
"My other wish, my other dream, is to one day coach Barca. That's the truth.
"I now owe to Everton. We have a very powerful and exciting project and we will reinforce our best to try to reach next season the Champions League."