The magnetization reversal in magnetic FePt nanoelements having Reuleaux 3D geometry is studied using micromagnetic simulations employing Finite Element discretizations. Magnetic skyrmions are revealed in different systems generated by the variation of the magnitude of the magnetocrystalline anisotropy which was kept normal to the nanoelement's base and parallel to the applied external field. The topological quantity of skyrmion number is computed in order to characterize micromagnetic configurations exhibiting skyrmionic formations. Micromagnetic configurations with a wide range of skyrmion numbers between -3 and 3 are indicative for the existence of one or multiple skyrmions that have been detected and stabilized in a range of external fields. Internal magnetic structures are shown consisting of Bloch type skyrmionic entities in the bulk altered to Néel skyrmions on the nanoelement's bottom and top base surfaces. The actual sizes of the formed skyrmions and the internal magnetization structures were computed. In particular, the sizes of the generated and persistent skyrmions were calculated as functions of the magnetocrystalline anisotropy value and of the applied external magnetic field. It is shown that the size of skyrmions is linearly dependent on the external field value. The slope of the linear curve can be controlled by the magnetocrystalline anisotropy value. The magnetic skyrmions can be created for FePt magnetic systems lacking of chiral interactions by designing the geometry-shape of the nanoparticle and by controlling the value of magnetocrystalline anisotropy.