Lillie, Jackson and Willsher Weekes died in the 2012 fire at Villaggio Mall in Doha.
The Doha News reports that Qatar's Court of Cassation has overturned the earlier decision to acquit the defendants of voluntary manslaughter and has ordered a retrial.
The group to go back on trial include the co-owners of Gympanzee daycare, the place where the triplets and 16 others died.
Also facing a third trial will be Villiagio's chairman and manager, and a municipal employee.
The case is expected to be heard by the Court of Appeal.