Divertor Tokamak Test Facility (DTT) is a new European superconducting tokamak, currently under final design, addressed to investigate alternative power exhaust solutions for DEMO. Although the divertor system is not finalized yet, the machine and port geometry set limitations on the divertor pumping system operational space. A numerical study of neutral gas dynamics in the divertor region is performed based on the DSMC method by applying the DIVGAS code. The study includes both single-null (SN) and double-null (DN) divertor configurations. For both configurations, the SolEdge2D–EIRENE plasma simulations have been performed for a deuterium plasma with neon seeding and the extracted information about the neutral particles on the predefined interfaces is imposed as incoming boundary conditions for DIVGAS simulations. In the SN case, two plasma puffing scenarios and three candidate pumping port arrangements have been considered. The divertor dome influence on the pumped fluxes can reach 50%. An increase of the capture coefficient six times leads to a decrease in the pressure at the pumping openings by a factor of about 4.5–7. The influence of the size of the lower vertical opening has been studied showing that the enlarged vertical port may establish as the main pumping opening. In the DN case, when the pumping is performed from both lower and upper divertor the overall pumped fluxes at the upper divertor are always higher than the corresponding ones for the lower divertor by a factor of 2–2.5, mainly due to the difference in the pumping areas. In both SN and DN cases, the neutrals outflux toward the X-point dominates the particle transport in the private flux region. The operational space provided by this first assessment is relatively stable against modified classical divertor geometries and allows a more thorough assessment of the pumping technology of the DTT fusion device in the future.