We calculate the trispectrum Tζ (k1 , k2 , k3, k4) of the primordial curvature perturbation ζ, gener­ated during a slow-roll inflationary epoch and considering a quadratic two-component scalar potential and canonical kinetic terms. We consider one-loop and tree leve] contlibutions, and show that it is pos­sible to attain observable values for the leve! of non-gaussianity T N L, if Tζ; is dominated by the one-loop contlibution. This work is performed by taking into account that there exists sorne physical restrictions that constrain the available parameter window. Such conditions are: thc existence of sorne coupling constants that guarantee the calculation in a perturbative regime, the relative weight of the one-loop and tree leve! contributions, the normalisation of the spectrum, the observed spectral index, and the mini mal amount of inflation required to solve the horizon problem.