In this paper we construct and study discretizations of an extension of the Zakharov system occurring in plasma physics. This system is intermediate between Euler-Maxwell and Zakharov systems. The usual Zakharov system can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process and that are asymptotic preserving. We prove some stability and convergence results and we perform some numerical tests showing that the range of validity of the extended system is wider than that of the usual Zakharov system.