The former defender, who spent six years at the Nou Camp between 1989 and 1995, has regularly been linked with a return to his old club after Luis Enrique announced he was stepping down at the end of the season.
Koeman, in the first season of a three-year contract having arrived from Southampton last summer, has previously dismissed the Barcelona links and stressed he has a job to do on Merseyside.
However, that has not stopped him admitting his ambitions stretch to a return to the Spanish giants.
"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 Catalan newspaper Sport.
Read the full article on eurosport.co.uk: Ronald Koeman: My dream is to coach Barcelona