  HESS J1804-216 is one of the brightest yet most mysterious TeV gamma-ray
sources discovered to date. Previous arc-minute scale studies of the
interstellar medium (ISM) surrounding this TeV gamma-ray source revealed HESS
J1804-216 is likely powered by a mature supernova remnant (SNR) or pulsar,
hence its origin remains uncertain. In this paper, we focus on the diffusive
escape of cosmic-ray protons from potential SNR accelerators. These cosmic rays
interact with the ISM to produce TeV gamma-rays. We utilise the isotropic
diffusion equation solution for particles escaping from a shell, to model the
energy-dependent escape and propagation of protons into the ISM. This work is
the first attempt at modelling the spatial morphology of gamma-rays towards
HESS J1804-216, using arc-minute ISM observations from both Mopra and the
Southern Galactic Plane Survey. The spectral and spatial distributions of
gamma-rays for the two nearby potential SNR counterparts, SNR G8.7-0.1 and the
progenitor SNR of PSR J1803-2137, are presented here. We vary the diffusion
parameters and particle spectrum and use a grid search approach to find the
best combination of model parameters. We conclude that moderately slow
diffusion is required for both candidates. The most promising candidate to be
powering the TeV gamma-rays from HESS J1804-216 in a hadronic scenario is the
progenitor SNR of PSR J1803-213.
