We evaluate the performance of relay selection over Nakagami-m fading channels in the presence of a cluster of full-duplex decode-and-forward relays with self-interference. Specifically, we derive the exact cumulative distribution function of the end-to-end signal-to-interference-plus-noise ratio in the presence of a direct source-destination link. When a direct link exists, all dual-hop paths become mutually correlated due to the common direct-link interference. The presented exact results enable the evaluation of the outage performance and system throughput for fixed-rate transmission systems. The theoretical findings are verified by numerical simulations, where the severity of fading effect in the residual self-interference link is also discussed.