A high-frequency asymptotic solution based on the Uniform Geometrical Theory of Diffraction (UTD) is proposed for the surface fields excited by a magnetic source located on the surface of a sphere with an impedance boundary condition. The assumed large parameters, compared to the wavelength, are the radius of the sphere and the distance between the source and observation points along the geodesic path, when both these points are located on the surface of the sphere. Different from the UTD-based solution for a perfect electrically conducting sphere, some higher-order terms and derivatives of Fock type integrals are included as they may become important for certain surface impedance values as well as for certain separations between the source and observation points. This work is especially useful in the analysis of mutual coupling between conformal slot/aperture antennas on a thin material coated or partially coated sphere.