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In this paper, we investigate two user scheduling algorithms (optimal user and threshold-based user scheduling algorithms) when we consider potential eavesdroppers in an uplink wiretap network. The optimal user scheduling (OUS) algorithm selects the user who has the maximum secrecy rate, based on channel feedback from all users. On the other hand, the threshold-based user scheduling (TUS) algorithm first considers the information leakage from the users to potential eavesdroppers and then selects the user among candidates who satisfy a threshold criterion on the information leakage. The OUS algorithm shows an optimal performance in terms of secrecy rate, but the TUS algorithm can achieve secrecy rate comparable with the OUS algorithm with reduced feedback overhead. For main contributions, we mathematically analyze the asymptotic behavior of the achievable secrecy rate of two scheduling algorithms when the signal-to-noise ratio (SNR) approaches to infinity. Further, we derive the approximated secrecy rate of the TUS algorithm and propose criteria to determine threshold values which maximize the achievable secrecy rate of the TUS algorithm. We verify our analytical results through simulations. We perform an extra simulation to investigate the effect of channel estimation error in the wiretap links on the average secrecy rate. Due to different scheduling principles in OUS and TUS schemes, the TUS scheme yields robustness against the channel estimation error in the wiretap links, compared with the OUS schemes.