We analyze the outage performance of relay selection in two-way full-duplex amplify-and-forward cooperative systems in the presence of residual loop-interference (LI) over Nakagami-m fading channels. In the proposed system, a relay node is selected according to max-min policy and the physical-layer-network-coding technique is applied for two-way transmission. By using end-to-end signal-to-interference-plus-noise-ratio, a new exact outage probability expression is derived in a single-integral form. The numerical and Monte-Carlo simulation results verify the analysis. Moreover, lower-bound and asymptotic expressions for the outage probability are obtained in closed-form. The numerical results reveal that the max-min selection policy provides a significant performance improvement for two-way full-duplex relaying. We observe that the outage performance can be enhanced as long as either the number of relay nodes, the transmit power, or the efficiency of the LI cancellation process increases.