Numerous complexes between versatile derivatives of metalloporphyrins MP (with M being Mn, Co, Ni, Cu, Zn and Fe) and C60 have been synthesized and characterized recently. Favorable van der Waals attractions between the curved π-surface of the fullerene and the planar π-surface of MP assist in the supramolecular recognition, overcoming the necessity of matching a concave-shaped host with a convex-shaped guest structure. Recently, we reported the computational studies of the structures and electronic properties of the series of metalloporphyrins where all the four pyrrole nitrogen atoms are replaced with P-atoms, MP(P)4, M = Sc-Zn. Motivated by the numerous examples of the complex formation between regular planar or quasi-planar MP and C60, we computationally investigated possibility of the complex formation between two MP(P)4 species, ZnP(P)4 and NiP(P)4, and C60 without any linkers, using the CAM-B3LYP/6-31G* approach, both in the gas phase and with implicit effects from C6H6. We found that the binding energies in the MP(P)4-C60 complexes for these two MP(P)4 compounds are relatively low, ca. 1-1.6 kcal/mol and ca. 5 kcal/mol for M = Zn and Ni, respectively. The ZnP(P)4 species was found to be noticeably distorted in the ZnP(P)4-C60 complex whereas NiP(P)4 inside the NiP(P)4-C60 complex essentially retained its bowl-like shape. Thus, we showed the possibility of the formation of complexes between MP(P)4 species and C60 without any linkers and showed dependence of the complex stability on the transition metal M. Further investigations are in progress.