Processing multi-million tokens for advanced Large Language Models (LLMs) poses a significant memory bottleneck for existing AI systems. This bottleneck stems from a fundamental resource imbalance, where enormous memory capacity and bandwidth are required, yet the computational load is minimal. We propose NELSSA (Processing Near Memory for Extremely Long Sequences with Sparse Attention), an architectural platform that synergistically combines the high-capacity Processing Near Memory (PNM) with the principles of dynamic sparse attention to address this issue. This approach enables capacity scaling without performance degradation, and our evaluation shows that NELSSA can process up to 20M-token sequences on a single node (Llama-2-70B), achieving an 11× to 40× speedup over a representative DIMM-based PNM system. The proposed architecture radically resolves existing inefficiencies, enabling previously impractical multi-million-token processing and thus laying the foundation for next-generation AI applications.