The prewetting phenomena in a nematic liquid crystal confined to a droplet embedded in a spherical solid surface are discussed. This paper is based on Landau-de Gennes theory and Nobili-Durand surface energy. By using a Maxwell construction, we find that the first-order boundary-layer transition inside of droplet which vanishes completely below a critical radius Rc when bulk nematic isotropic transition temperature is approached from above. We obtain a narrow temperature interval above the bulk nematic-isotropic phase transition which corresponds to nematic boundary layer inside of droplet. The interval length depends on surface potential and droplet radius. We also find that there is no critical radius for boundary transition when the nematic-isotropic transition temperature is approached from below.