In a market driven by Lévy processes, we consider an optimal portfolio problem for a dealer who has access to some information in general smaller than the one generated by the market events. In this sense we refer to this dealer as having partial information. For this generally incomplete market and within a non-Markovian setting, we give a characterization for a portfolio maximizing the expected utility of the final wealth. Techniques of Malliavin calculus are used for the analysis.