The fluid antenna system (FAS) has emerged as a disruptive technology that promises outstanding diversity and multiplexing gains comparable to or better than multiple-input multiple-output (MIMO), but without the issues of channel state information (CSI) acquisition and the advantage of requiring smaller physical spaces of upcoming user devices. This work investigates the potentialities of this technology to provide secure transmissions by analysing the secrecy outage probability (SOP) of two different implementations of FAS undergoing spatial correlated Nakagami-m fading by assuming i) non-diversity FAS and maximum-gain combining-FAS (MGC-FAS) diversity scheme at the legitimate node and ii) multiple-antennas performing maximal ratio combining (MRC) at the eavesdropper. Specifically, using a novel asymptotic matching method, a simple and accurate closed-form approximations to the end-to-end signal-to-noise-ratio (SNR) distributions are derived in terms of well-known functions without incurring tricky functions or multi-fold integrals. Our findings reveal that the secrecy performance of the MGC-FAS beats the non-diversity FAS counterpart only when i) the antenna size of the FAS tube is large enough, and ii) the average SNR of the legitimate path is much greater than that of the eavesdropper link. Finally, numerical results validate our approximations of the SOP for the MGC-FAS scheme and demonstrate its accuracy under different FAS conditions.