Rigid spheres with a short-range attractive potential are taken as a coarse-grained model of vesicles, which contain a solution of semiflexible polymers in their interior. Assuming good solvent conditions with an implicit description of the solvent, effective monomers experience bond-length and bond-angle potentials as well as excluded-volume interaction. Due to the attractive vesicle surface, phase separation occurs between a thin shell of adsorbed monomers at the surface and a rather dilute, and therefore, disordered polymer solution in the sphere interior. While at a planar attractive surface the wormlike chains would exhibit liquid crystalline (nematic and smectic) order, the curvature of the sphere frustrates this order, causing the existence of defects in the orientational order. In the dense monolayer of surface-attached polymers, the stiff chains acquire a curvature corresponding to banana-like shapes for rather small contour length, causing a local nematic order of biaxial type. These orderings are compared to related phenomena in spheres densely filled with semiflexible polymers. We complement the results obtained by Molecuar Dynamics simulations by corresponding Density Functional Theory calculations. (C) 2018 Elsevier Ltd. All rights reserved.