"By making Starbucks' presence very visible to the community, it could attract unwanted guests to the school," one father, who wished to remain anonymous, told the paper.
Headmaster Stephen Chynoweth wrote to parents to confirm the Starbucks trial and reassure them that all staff had been vetted and approved to work in schools.
According to the report, the shop's profits will be shared with the school and used to pay for new equipment and other school initiatives.
Some parents are in support of the move and have posted comments on the community website www.expatwoman.com saying as much. GEMS's marketing director, Richard Forbes, told the paper he was "aware of the very positive feedback from other parents".
Dubai Knowledge and Human Development Authority said it was an internal school matter and that no complaints about it had been received from parents.