Acquiring the status information of candidate servers is important for decision making in edge computing, which is however extremely challenging and time-consuming in high-dense device-assisted task offloading scenarios. In this paper, we propose a Distributed Status-aware response (DiSar) method to balance the status acquisition and task execution latency by utilizing incomplete but necessary status information. Specifically, each candidate server device set a backoff timer based on their computing and transmission status independently, which enables low-latency servers to rapidly respond while avoiding wireless transmission collisions. A salient-driven status mapping algorithm is proposed for the backoff timer setting, and the performances of DiSar are analyzed theoretically. Accordingly the influencing parameters are further optimized to rapidly fit the dynamic offloading environment, whereby the performances of DiSar are guaranteed. Simulation results demonstrate that DiSar can find the optimal server device with 95% probability while reducing the information acquisition latency by 96.33%, compared with centralized complete information acquisition. In addition, the overall task offloading latency can be reduced by 11.63% to 52.67%, using DiSar compared with the state-of-theart methods.