As intuitive units of speech, syllables have been widely studied in linguistics. A syllable can be defined as a three-constituent unit with a vocalic centre surrounded by two (in some languages optional) consonant clusters. Syllables are also used to design automatic speech recognition (ASR) models. The significance of knowledge-driven syllable-based tokenisation in ASR over data-driven byte-pair encoding has often been debated. However, the emergence of transformer-based ASR models employing self-attention (SA) overshadowed this debate. These models learn the nuances of speech from large corpora without prior knowledge of the domain; yet, they are not interpretable by design. Consequently, it is not clear if the recent performance improvements are related to the extraction of human-interpretable knowledge. We probe such models for syllable constituents and use an SA head pruning method to assess the relevance of the SA weights. We also investigate the role of vowel identification in syllable constituent probing. Our findings show that the general features of syllable constituents are extracted in the earlier layers of the model and the syllable-related features mostly depend on the temporal knowledge incorporated in specific SA heads rather than on vowel identification.