In principle, numerical simulations of boundary value problems that involve fluid-soil interaction should account for the evolution of permeability due to soil deformation. For many applications of interest in geotechnical engineering, an accurate assessment of the permeability is key to an accurate prediction of settlements and pore water pressure changes. Finite element models rely on laboratory or field testing to characterise permeability; however, these methods cannot easily evaluate anisotropy or moderate variations of permeability. Current testing tools have a limited accuracy and a rigid experimental set-up, and are usually restricted to consider one flow direction. In this study, the influence of shearing on the intrinsic permeability and the anisotropy of permeability in medium-loose liquefiable sands is investigated. The discrete element method (DEM) was used to simulate monotonic undrained and drained triaxial test simulations on model soils comprising spherical particles. The particle positions were recorded at discrete strain levels and the data were taken as input into finite volume method (FVM) simulations which were used to evaluate intrinsic permeability in selected subsamples. In the FVM simulations, permeability was evaluated in the three orthogonal directions. The results indicate that shear deformation induces an anisotropy in permeability, in both drained and undrained triaxial conditions and this anisotropy increases with axial strain. Specifically, the results show an increase in permeability in the direction of the major principal stress, whereas a reduction permeability is observed in the orthogonal plane. Undrained simulations exhibit a jump in vertical permeability around the liquefaction onset; this can be attributed to the sudden loss of particle contacts.