The studio believes that structural glass could be used to create formally identical versions of the parts of the Paris building destroyed in the fire on 15 April.
"I believe this definitive example of French gothic architecture requires a deep respect and appreciation of the history and intent of the original design," said Tim Kobe, founder and CEO of Eight Inc.
"Its proportions, scale and detail brings life to the architecture," he added. "It should not be about the ego of a new architectural expression but a solution to honour this historic structure."
Eight Inc is best known for working with Steve Jobs to develop the concept for the first Apple Stores, which opened in 2001.
Like the Apple Stores, this latest proposal centres around the idea of transparency. Structural glass is thicker and tougher than standard glass, so it can be installed without the visual mess of a supporting framework.
Kobe's team believes glass offers the best opportunity to respect the scale and texture of the original design, while also invoking "the memory and temporal nature of the building".
"The spiritual and luminous qualities of the material allows for both the accurate representation of the form of the original design but also implies the impermanence of architecture and the impermanence of life," reads the project description.
Since the fire, there have been numerous ideas proposed for the French gothic cathedral, ranging from the interesting to the outrageous. Architect Vincent Callebaut proposed a roof that generates energy and food, while Studio Fuksas suggested building a new structure using crystal.
Meanwhile designer Sebastian Errazuriz suggested turning the cathedral into a space-rocket launchpad, in a bid to stop architects producing any more designs.
Although the French senate wants the historic structure to be rebuilt exactly as it last was, French president Emmanuel Macron is keen for "an inventive reconstruction". His prime minister, Edouard Philippe, had previously announced that there would be a design competition.