An analytical approach is developed for assessing the confinement of fusion alphas born in the plasma core of a tokamak-reactor with a toroidal current hole. Confinement criteria determining the minimum plasma current requirements with respect to the alpha particle energy are derived. It is shown that the enhancement of first orbit alpha losses induced by a current hole of a radius r* can be recompensed by an increase of the total plasma current by the factor 1/(1- r*/a), where a is the minor plasma radius. Numerical modelling of alpha losses in an equilibrium magnetic configuration reconstructed for a high-performance JET current hole plasma validates the analytical results.