Despite the fact that no chick is expected, Drost said the males are carefully tending the nest.
"Both birds brood on the eggs, they guard the nest alternately," he said in a statement on the zoo's website.
Same-sex pairings are not uncommon in penguins, and there have been instances of gay couples successfully hatching eggs.
A Sydney couple, Sphen and Magic, hatched and raised an egg at the city's Sea Life Aquarium.
The pair of Gentoo parents had always been close, collecting pebbles to build a nest during mating season.
Sphen even gave Magic a special stone to cement their relationship.
In 2017, a penguin chick was raised by two "mums" at Kelly Tarlton's aquarium in Auckland.
The aquarium fostered the chick with the two female king penguins after the chick's mother, Shaq, was abandoned by her male partner.
The two females, dubbed Thelma and Louise after the classic 1991 Hollywood road film, were the only same-sex couple at Kelly Tarlton's at the time.