The transition towards quantum-safe cybersecurity requires organisations to assess their dependence on cryptographic mechanisms, identify vulnerabilities arising from quantum computing, and develop appropriate migration strategies. However, assessing organisational quantum-safe readiness requires the analysis of heterogeneous evidence distributed across cybersecurity policies, technical documentation, standards, governance documents, and other organisational resources. This project investigates the use of Large Language Models (LLMs) to support systematic and evidence-based assessment of organisational quantum-safe cybersecurity readiness. The research will examine the ability of LLMs to extract relevant evidence from textual documents, map the extracted information to defined quantum-readiness dimensions and indicators, and support structured readiness assessment. Particular attention will be given to post-quantum cryptography, cryptographic migration, governance, asset and dependency identification, policy readiness, and organisational transition planning. The study will experimentally evaluate different LLM configurations and prompting strategies and investigate their reliability, consistency, explainability, and agreement with reference assessments. Where appropriate, parameter-efficient fine-tuning approaches will also be investigated to determine whether domain adaptation improves evidence extraction and readiness assessment. The expected outcome is a reproducible AI-assisted framework for analysing quantum-safe readiness from documentary evidence, together with an empirical understanding of the capabilities and limitations of LLMs for cybersecurity assessment. The computational resources may additionally support closely related AI-assisted cybersecurity experiments, while LLM-based quantum-safe readiness assessment will remain the primary research focus.