Neural audio signal codecs have attracted significant attention in recent years. In essence, the impressive low bitrate achieved by such encoders is enabled by learning an abstract representation that captures the properties of encoded signals, e.g., speech. In this work, we investigate the relation between the latent representation of the input signal learned by a neural codec and the quality of speech signals. To do so, we introduce Latent-representation-to-Quantization error Ratio (LQR) measures, which quantify the distance from the idealized neural codec's speech signal model for a given speech signal. We compare the proposed metrics to intrusive measures as well as data-driven supervised methods using two subjective speech quality datasets. This analysis shows that the proposed LQR correlates strongly (up to 0.9 Pearson's correlation) with the subjective quality of speech. Despite being a non-intrusive metric, this yields a competitive performance with, or even better than, other pre-trained and intrusive measures. These results show that LQR is a promising basis for more sophisticated speech quality measures.