The former Netherlands international would welcome the chance to return to the Camp Nou side after a previous successful spell as a player
The Catalans are believed to be considering parting company with current head coach Gerardo Martino at the end of the season and Sport reported earlier this week that Koeman is one of the main candidates to succeed the Argentine.
Koeman, who wore the Barcelona jersey between 1989 and 1995 during his active career, recently revealed that he will leave Feyenoord this summer after three years in charge and he has made it clear that a return to Camp Nou would be an interesting option.
"Would I be interested in taking charge of Barcelona? Yes, of course," Koeman told NOS.
"But they have not approached me yet."
The 51-year-old Koeman enjoyed relatively successful coaching spells at Vitesse, Ajax, Benfica and PSV before his reputation took a blow at Valencia and AZ.
The former Netherlands international has since gotten back on his feet at Feyenoord, however, guiding the fallen Rotterdam giants to three consecutive top three finishes.