This paper presents an FPGA-friendly approach to tracking elephant flows in network traffic. Our approach, Single Step Segmented Least Recently Used (S3-LRU) policy, is a network traffic-friendly replacement policy for maintaining flow states in a Naïve Hash Table (NHT). We demonstrate that our S3-LRU approach preserves elephant flows: conservatively promoting potential elephants and evicting low rate flows in LRU manner. Our approach keeps flow-state of any elephant since start-of-day and provides a significant improvement over filtering approaches proposed in previous work. Our FPGA-based implementation of the S3-LRU in combination with an NHT suites well the parallel access to block memories while capitalising on the retuning of parameters through dynamic-reprogramming.