This paper considers the kind of introspection that large language models (LLMs) might be able to have. It argues that LLMs, while currently limited in their introspective capabilities, are not inherently unable to have such capabilities: they already model the world, including mental concepts, and already have some introspection-like capabilities. With deliberate training, LLMs may develop introspective capabilities. The paper proposes a method for such training for introspection, situates possible LLM introspection in the 'possible forms of introspection' framework proposed by Kammerer and Frankish, and considers the ethical ramifications of introspection and self-report in AI systems.