The use of a large apex-angle axicon for common-path interferometric wavefront sensing is proposed. The approach is a variant of point-diffraction interferometry bearing similarities to pyramidal wavefront sensing. A theoretical basis for wavefront sensing with an axicon is developed, and the outcomes of numerical simulations are compared to experimental results obtained with spherical and cylindrical ophthalmic trial lenses. It is confirmed that the axicon can be used for wavefront sensing, although its refraction may ultimately complicate and limit its operational range.