In quantum optomechanics, finding materials and strategies to limit losses has been crucial to the progress of the field. Recently, superfluid ${}^{}\mathrm{He}$ was proposed as a promising mechanical element for quantum optomechanics. This quantum fluid shows highly desirable properties (e.g., extremely low acoustic loss) for a quantum optomechanical system. In current implementations, superfluid optomechanical systems suffer from external sources of loss, which spoils the quality factor of resonators. In this work, we propose an alternate implementation, exploiting nanofluidic confinement. Our approach, based on acoustic resonators formed within phononic nanostructures, aims at limiting radiation losses to preserve the intrinsic properties of superfluid ${}^{}\mathrm{He}$. In this work, we estimate the optomechanical system parameters. Using recent theory, we derive the expected quality factors for acoustic resonators in different thermodynamic conditions. We calculate the sources of loss induced by the phononic nanostructures with numerical simulations. Our results indicate the feasibility of the proposed approach in a broad range of parameters, which opens prospects for more complex geometries.