  Magnetic monopoles have been a subject of study for more than a century since
the first ideas by A. Vaschy and P. Curie, circa 1890. In 1974, Y. Nambu
proposed a model for magnetic monopoles exploring a parallelism between the
broken symmetry Higgs and the superconductivity Ginzburg-Landau theories in
order to describe the pions quark-antiquark confinement states. There, Nambu
describes an energetic string where its end points behave like two magnetic
monopoles with opposite magnetic charges -- quark and antiquark. Consequently,
not only the interaction among monopole and antimonopole, mediated by a massive
vector boson (Yukawa potential), but also the energetic string (linear
potential) contributes to the effective interaction potential. We propose here
a monopole-antimonopole non confining attractive interaction of the Nambu-type,
and then investigate the formation of bound states, the monopolium. Some
necessary conditions for the existence of bound states to be fulfilled by the
proposed Nambu-type potential, Kato weakness, Set\^o and Bargmann conditions,
are verified. In the following, ground state energies are estimated for a
variety of monopolium reduced mass, from $10^2$MeV to $10^2$TeV, and Compton
interaction lengths, from $10^{-2}$am to $10^{-1}$pm, where discussion about
non relativistic and relativistic limits validation is carried out.
