In this correspondence, we consider a confidential communication through slow non-selective correlated Rayleigh fading channel, where a single antenna transmitter communicates at a pre-decided constant rate with a legitimate receiver in the presence of an eavesdropper. Both the legitimate receiver and eavesdropper are equipped with multiple antennas and employ maximal ratio combining (MRC) reception scheme. With the presence of channel diversity, we find the closed-form expressions for the probability of non-zero secrecy capacity and the outage probability of secrecy capacity in terms of channel parameters such as correlation coefficient and the ratio of main and eavesdropper channel gains that will be called average channel gain ratio (CGR). The analysis of secure outage performance with the MRC diversity scheme tells how the channel diversity enhances the secrecy capacity. We quantify the effect of antenna correlation on the probability of positive secrecy capacity and the secure outage probability. We also investigate how the target secrecy rate influences the effect of antenna correlation on the secure outage probability. Moreover, as a result of obtaining the closed-form expressions for the probability of positive secrecy capacity and the outage probability, it is insightful to see how the channel parameters affect the secure outage performance of the correlated channels.