The basic philosophy behind data assimilation forecasting is that accurate knowledge of the initial conditions at the beginning of the forecast will produce reliable predictions. In this work we explore this idea under the assumption that El Ni¿o--Southern Oscillation (ENSO) behaves as a stochastically forced phenomenon using the Kleeman intermediate model. This work provides a quantification of how the stochastic forcing (SF) is a limiting factor in increasing the predictability of ENSO via data assimilation in this intermediate model. Different cases are considered corresponding to the presence or absence of SF during different stages of the forecast process (i.e., assimilation and prediction or validation). Within each case, different strong-constraint assimilation methodologies are used. These methodologies show that better results can be obtained when information about the thermal structure of the upper ocean is considered and when interaction between the atmosphere and ocean is allowed in the assimilation process. Considering the best possible scenario, where observations of heat content are available at every grid point and time step, the presence of SF decreases the skill of the forecasts to about 12 months. This is similar to the skill reported by many operational and experimental seasonal prediction systems that use strong-constraint data assimilation. Therefore our results suggest that there is little room for improvement in forecast skill as a result of strong-constraint data assimilation.