Recent Serverless workloads tend to be largescaled/CPU-memory intensive, such as DL, graph applications, that require dynamic memory-to-compute resources provisioning. Meanwhile, recent solutions seek to design page management strategies for multi-tiered memory systems, to efficiently run heavy workloads. Compute Express Link (CXL) is an ideal platform for serverless workloads runtime that offers a holistic memory namespace thanks to its cache coherent feature and large memory capacity. However, naively offloading Serverless applications to CXL brings substantial latencies. In this work, we first quantify CXL impacts on various Serverless applications. Second, we argue the opportunity of provisioning DRAM and CXL in a fine-grained, application-specific manner to Serverless workloads, by creating a shim layer to identify, and naively place hot regions to DRAM, while leaving cold/warm regions to CXL. Based on the observation, we finally propose the prototype of Porter, a middleware in-between modern Serverless architecture and CXL-enabled tiered memory system, to efficiently utilize memory resources, while saving costs.