Colloidal suspensions containing magnetic nanoparticles placed in appropriate carrier liquids present strong magnetic dipoles. These suspensions, in general, exhibit normal liquid behaviour coupled with super paramagnetic properties. This leads to the possibility of remotely controlling the flow of such liquids with a moderate-strength external magnetic field. In this study, we numerically investigate the viability of controlling and steering a base-fluid with magnetic-sensitive nanoparticles into randomly structured fibrous porous media. Three dimensional flow simulations are performed using the lattice Boltzmann method. The simulation results for the flow front are presented, and the effect of the magnetic field strength on the rate of ferrofluid penetration is discussed. It is shown that the porosity of the porous medium and the size of the fibres have a strong effect on the ferrofluid penetration rate.