Large Language Models (LLM) have demonstrated the capability of generating free text self Natural Language Explanation (self-NLE) to justify their answers. Despite their logical appearance, self-NLE do not necessarily reflect the LLM actual decision-making process, making such explanations unfaithful. While existing methods for measuring self-NLE faithfulness mostly rely on behavioral tests or computational block identification, none of them examines the neural activity underlying the model's reasoning. This work introduces a novel flexible framework for quantitatively measuring the faithfulness of LLM-generated self-NLE by directly comparing the latter with interpretations of the model's internal hidden states. The proposed framework is versatile and provides deep insights into self-NLE faithfulness by establishing a direct connection between self-NLE and model reasoning. This approach advances the understanding of self-NLE faithfulness and provides building blocks for generating more faithful self-NLE.