Mitigating the effects of wind turbine wakes is a central part of wind farm design. This paper proposes a spectral solver for the axisymmetrical Ainslie wake model based on modified Laguerre basis functions over the semi-infinite radial domain and a marching scheme in the downstream direction. This orthogonal basis promises fast convergence and a low number of DOFs for discretizing the continuity and axial momentum equation, promising a computationally efficient method. The numerical implementation of the model could not be finished in time; preliminary results are presented but still show non-negligible conservation errors. The focus of this work lies, therefore, on a detailed derivation of the method and a discussion of the sources of numerical errors in the nonlinear terms, and due to the truncation of the spectral basis, a comparison of the solver outputs to other methods remains part of the ongoing work.