We present ContextPrefetcher, a host-guided high-performant prefetching framework for near-storage accelerators that prefetches data blocks from storage (e.g., NAND) to devicelevel RAM. Efficiently prefetching data blocks to device-level RAM reduces storage access costs and improves I/O performance. We introduce a novel abstraction, Cross-layered Context (CLC), a virtual entity that spans across the host and the device and is used for identifying, managing, and tracking active and inactive data such as files, objects (within object stores), or a range of blocks. To support efficient prefetching of actively used CLCs to device memory without incurring near-device resource (memory and compute) bottlenecks, ContextPrefetcher delegates prefetching management to the host, guiding near-device compute to prefetch blocks of active CLC. Finally, ContextPrefetcher facilitates the swift reclamation of blocks associated with inactive CLC. Preliminary evaluation against state-of-the-art near-storage accelerator designs demonstrates performance gains of up to 1.34×.