Domain generation algorithms enable resilient malware communication by generating pseudo-random domain names. While traditional detection relies on task-specific algorithms, the use of Large Language Models (LLMs) to identify Algorithmically Generated Domains (AGDs) remains largely unexplored. This work evaluates nine LLMs from four major vendors in a zero-shot environment, without fine-tuning. The results show that LLMs can distinguish AGDs from legitimate domains, but they often exhibit a bias, leading to high false positive rates and overconfident predictions. Adding linguistic features offers minimal accuracy gains while increasing complexity and errors. These findings highlight both the promise and limitations of LLMs for AGD detection, indicating the need for further research before practical implementation.