Imaging and manipulating the spin structure of nano- and mesoscale magnetic systems is a challenging topic in magnetism, yielding a wide range of spin phenomena such as skyrmions, hedgehog-like spin structures, or vortices. A key example has been provided by the vortex spin texture, which can be addressed in four independent states of magnetization, enabling the development of multibit magnetic storage media. Most of the works devoted to the study of the magnetization reversal mechanisms of the magnetic vortices have been focused on micrometer-size magnetic platelets. Here we report the experimental observation of the vortex state formation and annihilation in individual 25 nm molecular-based magnetic nanoparticles measured by low-temperature variable-field magnetic force microscopy. Interestingly, in these nanoparticles the switching of the vortex core can be induced with very small values of the applied static magnetic field.