Tribulietx led Auckland to the bronze medal in last year's FIFA Club World Cup, beating Mexico's Cruz Azul on penalties in the play-off for third.
Roar football director Ken Stead visited New Zealand last month to interview Tribulietx, The Courier-Mail reports.
The 42 year-year old Spaniard is currently with Auckland City in Fiji at the Oceania Champions League, where it plays Team Wellington in Sunday's final and is chasing a fifth successive title.
Dutchman Thijssen was named interim coach at the Roar in November last year, after Mike Mulvey was sacked six weeks into the new season, but the club's chairman Chris Fong told The World Game a new coach would be in charge for next season.
The previous season, Mulvey was named A-League coach of the year after leading Brisbane to the premiership-championship double.
Brisbane sits seventh in this year's A-League, but will make the finals as third-placed Perth Glory us ineligible due to salary cap breaches.
Roar is expected to announce their new coach next month.
