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A critical issue in optical chaos-based communications is the possibility to identify the parameters of the chaotic emitter and, hence, to break the security. In this paper, we study theoretically the identification of a chaotic emitter that consists of a semiconductor laser with an optical feedback. The identification of a critical security parameter, the external-cavity round-trip time (the time delay in the laser dynamics), is performed using both the auto-correlation function and delayed mutual information methods applied to the chaotic time-series. The influence on the time-delay identification of the experimentally tunable parameters, i.e., the feedback rate, the pumping current, and the time-delay value, is carefully studied. We show that difficult time-delay-identification scenarios strongly depend on the time-scales of the system dynamics as it undergoes a route to chaos, in particular on how close the relaxation oscillation period is from the external-cavity round-trip time.