We investigate the possibility of electron pairing in metallic nanoparticles containing a few hundreds of atoms at zero temperature. In these particles both electrons and phonons are mesoscopic, i. e. modified by the nanoparticles finite size. The electrons, the phonons, and their interaction are described within the framework of a simplified model. The effective electron-electron interaction is derived from the underlying electron-phonon interaction. The effect of both effective interaction and Coulomb interaction on the electronic spectrum is evaluated. Results are presented for aluminum nanoparticles containing 100 to 400 atoms.