The problem of the existence of bound states outside the continuum of the bands due to the presence of a nonlinear impurity is studied within a two-band tight-binding model in one dimension. The nonlinear impurity deviates from the ordinary sites by an on-site energy of the form , where is the probability of finding the particle at the impurity site, is referred to as the strength and is the nonlinearity of the impurity. For , there exist threshold values for below which there is no bound state. For , there is always one bound state above the upper band for ; and two bound states, one with energy inside the band gap and another below the lower band, for . For , there is always a bound state above (below) the upper (lower) band for . For , there is always a state inside the gap; while for , there exists an upper bound for above which no bound states are found inside the gap.