This paper investigates the space complexity of a self stabilizing leader election in a mediated population protocol (SS-LE MPP). Cai, Izumi and Wada (2009) showed that SS-LE in a population protocol (SS-LE PP) for n agents requires at least n agent-states, and gave a SS-LE PP with n agent-states for n agents. MPP is a model of distributed computation, introduced by Chatzigiannakis, Michail and Spirakis (2009) as an extension of PP allowing an extra memory on every agents pair. While they showed that MPP is stronger than PP in general, it was not known if a MPP can really reduce the space complexity of SS-LE with respect to agent-states. We in this paper give a SS-LE MPP with (2/3)n agent-states and a single bit memory on every agents pair for n agents. We also show that there is no SS-LE MPP with any constant agent-states and any constant size memory on each agents-pair for general n agents.