1I/'Oumuamua is the first interstellar interloper to be detected, and it shows a non-gravitational acceleration that cannot be accounted for by outgassing, given the strict upper limits of outgassing evident from Spitzer observations, unless the relative abundances of the common volatiles are very different to those in comets. As an alternative, it has been suggested that its peculiar acceleration is due to radiation pressure, requiring a planar-sheet geometry of an unknown natural or artificial origin. Here we assess whether or not the internal structure of 1I/'Oumuamua, rather than its geometry, could support a radiation-pressure-driven scenario. We adopt a mass fractal structure and find that the type of aggregate that could yield the required area-to-mass ratio would have to be extraordinarily porous, with a density ∼ 10 −5 g cm −3 . Such porous aggregates can naturally arise from the collisional grow of icy dust particles beyond the snowline of a protoplanetary disk, and we propose that 1I/'Oumuamua might be a member of this population. This is a hypothesis worth investigating because, if this were the case, 1I/'Oumuamua would have opened a new observation window on to the study of the building blocks of planets around other stars. This could set unprecedented constraints on planet formation models.