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ZrTe₅ is an interesting topological quantum material that is predicted to be a Dirac semimetal at the boundary between weak and strong topological insulator phases. In topological materials, it is highly desirable to control the doping of the material in order to adjust the Fermi level to coincide with features in the band structure. Since ZrTe₅ is a layered material, one approach to accomplishing this goal is “intercalation doping," in which a dopant diffuses between the layers of the material. We have used van der Waals-corrected density functional theory to investigate the intercalation of a variety of atoms into ZrTe₅ with the goal of identifying promising candidates for intercalation doping. We have calculated bulk absorption energies and diffusion barriers, and where bulk interlayer diffusion rates are reasonably rapid, we have also calculated the corresponding surface properties. We conclude that Li and Pd are promising candidates for intercalation doping of ZrTe₅.