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Autonomous AI agent systems are increasingly deployed as intermediaries between sensitive data sources and various external systems, creating significant privacy vulnerabilities during data transfer operations. Recent developments in large language model (LLM) agents and multi-agent collaborative frameworks have amplified these concerns, with traditional privacy-preserving approaches operating as external systems separate from agent architectures, resulting in security gaps, performance inefficiencies, and inadequate protection during dynamic agent interactions. This paper introduces a novel theoretical framework for an Agent-Specific Privacy Layer (ASPL) architecture that embeds anonymization capabilities directly within AI agent systems, ensuring comprehensive data protection throughout the agent operational lifecycle. The ASPL architecture comprises five integrated components: a Context-Aware Anonymization Engine, Privacy Knowledge Base, Reversible Transformation Module, Privacy Risk Assessment Component, and Audit and Compliance Tracker. Unlike traditional approaches that apply uniform transformations, the ASPL employs context-sensitive processing based on data characteristics, recipient identity, and exchange purpose, addressing recent challenges identified in federated multi-agent systems and LLM privacy research. We present comprehensive theoretical analysis, formal security proofs, and integration methodologies that establish foundations for privacy-first agent development in the era of autonomous AI systems.