The International Astronomical Union has not classified Varuna as a dwarf planet and has not addressed the possibility of officially accepting additional dwarf planets since the acceptance of Makemake and Haumea in 2008. Astronomer Gonzalo Tancredi considers Varuna as a likely candidate as it was thought to have a density greater than or equal to that of water () in order for it to be in hydrostatic equilibrium as a Jacobi ellipsoid. However, Tancredi has not made a direct recommendation for its inclusion as a dwarf planet. American astronomer Michael Brown considers Varuna to highly likely be a dwarf planet, placing it at the threshold of "highly likely". Based on a best-fit Jacobi ellipsoid model for Varuna, Lacerda and Jewitt estimate that Varuna has a low density of , slightly less than Tancredi's minimum density criterion. Despite this, Varuna was assumed to be in hydrostatic equilibrium in their model. Astronomer William Grundy and colleagues proposed that dark, low-density TNOs around the size range of approximately are likely partially differentiated with porous and rocky interiors. While the interiors of mid-sized TNOs such as Varuna likely had collapsed gravitationally, the surface remained uncompressed, implying that Varuna might not be in hydrostatic equilibrium.