This work investigates two strategies for zero-shot non-intrusive speech assessment leveraging large language models. First, we explore the audio analysis capabilities of GPT-4o. Second, we propose GPT-Whisper, which uses Whisper as an audio-to-text module and evaluates the naturalness of text via targeted prompt engineering. We evaluate the assessment metrics predicted by GPT-4o and GPT-Whisper, examining their correlation with human-based quality and intelligibility assessments and the character error rate (CER) of automatic speech recognition. Experimental results show that GPT-4o alone is less effective for audio analysis, while GPT-Whisper achieves higher prediction accuracy, has moderate correlation with speech quality and intelligibility, and has higher correlation with CER. Compared to SpeechLMScore and DNSMOS, GPT-Whisper excels in intelligibility metrics, but performs slightly worse than SpeechLMScore in quality estimation. Furthermore, GPT-Whisper outperforms supervised non-intrusive models MOS-SSL and MTI-Net in Spearman's rank correlation for CER of Whisper. These findings validate GPT-Whisper's potential for zero-shot speech assessment without requiring additional training data.