Radio observations of the τ Boötis system made with LOFAR in 2021 have been tentatively attributed to stellar wind-planet interactions between τ Boötis A and its planet. We apply a contemporaneous 2021 magnetic map of τ Boötis A obtained via Zeeman-Doppler imaging to examine the extent to which the radio observations can be understood as star-planet interactions. As exoplanet radio emission mechanisms depend greatly on the magnetic field geometry of the star-planet system, and on the power of the stellar wind in which the exoplanet is embedded, we create a fully three-dimensional magnetohydrodynamical model of the τ Boötis A system. Our model is constrained by the magnetic map geometry and incorporates Alfvén wave coronal heating and wind acceleration. Our model suggests that the large-scale magnetic field of τ Boötis A is too weak to produce radio signals as powerful the 2021 LOFAR observation.