  Inspired by the recent observation of a narrow resonance-like structure
around 2360 MeV in the p+n to d + \pi 0 + \pi 0 cross section, the possibility
of forming a NN*(1440) quasi-molecular state is investigated by using a meson
exchange model in which the \pi, \sigma, \rho\ and \omega\ exchanges in t- and
u-channels are considered. By adopting the coupling constants extracted from
the relevant NN scattering and N*(1440) decay data, it is found that a
deuteron-like quasi-molecular state of NN*(1440) with a binding energy in the
range of from 2 to 67MeV can be formed. Therefore, it is speculated that the
observed structure around 2360 MeV might be or may have a large component of
the NN*(1440) quasi-molecular state.
