Aim: Wireless Mesh Networks (WMN__ampersandsignrsquo;s) are gaining recognition among users. But WMN resources are not always utilized up to their full capacity. Redundant links and nodes can be turned in low power state for energy savings. WMN__ampersandsignrsquo;s build on IEEE 802.11s, supports link based power saving mode (PSM). But IEEE 802.11s standard does not specify switching among PSM. This research work provides a greedy approximation algorithm to allow redundant nodes and links in low power state to achieve minimum energy consumption. Methodology: Proposed algorithm is based on traffic consolidation over few nodes, subject to available link slots due to wireless interference. This will permit redundant nodes in deep sleep mode. Results: Analysis reveals that choosing power saving mode carefully of peer links can achieve great energy efficiency. Conclusion: Results signifies that energy saving comes with cost of delay. So traffic consolidation based approaches are more suitable for delay tolerant networks.