Large language models (LLMs) increasingly mimic human cognition in various language-based tasks. However, their capacity for metacognition - particularly in predicting memory performance - remains unexplored. Here, we introduce a cross-agent prediction model to assess whether ChatGPT-based LLMs align with human judgments of learning (JOL), a metacognitive measure where individuals predict their own future memory performance. We tested humans and LLMs on pairs of sentences, one of which was a garden-path sentence - a sentence that initially misleads the reader toward an incorrect interpretation before requiring reanalysis. By manipulating contextual fit (fitting vs. unfitting sentences), we probed how intrinsic cues (i.e., relatedness) affect both LLM and human JOL. Our results revealed that while human JOL reliably predicted actual memory performance, none of the tested LLMs (GPT-3.5-turbo, GPT-4-turbo, and GPT-4o) demonstrated comparable predictive accuracy. This discrepancy emerged regardless of whether sentences appeared in fitting or unfitting contexts. These findings indicate that, despite LLMs' demonstrated capacity to model human cognition at the object-level, they struggle at the meta-level, failing to capture the variability in individual memory predictions. By identifying this shortcoming, our study underscores the need for further refinements in LLMs' self-monitoring abilities, which could enhance their utility in educational settings, personalized learning, and human-AI interactions. Strengthening LLMs' metacognitive performance may reduce the reliance on human oversight, paving the way for more autonomous and seamless integration of AI into tasks requiring deeper cognitive awareness.