Modern approaches to enhancing Large Language Models' factual accuracy and knowledge utilization face a fundamental trade-off: non-parametric retrieval-augmented generation (RAG) provides flexible access to external knowledge but suffers from high inference latency and shallow integration, while parametric fine-tuning methods like LoRA risk catastrophic forgetting and degraded general capabilities. In this work, we propose MLP Memory, a lightweight parametric module that learns to internalize retrieval patterns without explicit document access. By pretraining an MLP to imitate a $k$NN retriever's behavior on the entire pretraining dataset, we create a differentiable memory component that captures the benefits of retrieval-based knowledge access in a fully parametric form. Our architecture integrates this pretrained MLP Memory with Transformer decoders through simple probability interpolation, yielding 17.5\% and 24.1\% scaling gains on WikiText-103 and Web datasets, respectively. It further achieves 12.3\% relative improvement on five question-answering benchmarks and 5.2 points absolute gain across nine general NLP tasks, while reducing hallucinations by up to 10 points on HaluEval. Moreover, MLP Memory delivers 2.5$\times$ faster inference than RAG with superior accuracy. Our findings show that learning retrieval patterns parametrically bridges the gap between efficient inference and effective knowledge access, offering a practical alternative to both RAG and fine-tuning approaches.