Recent advancements in large language models (LLMs) have revolutionized various domains, bringing significant progress and new opportunities. Despite progress in speech-related tasks, LLMs have not been sufficiently explored in multi-talker scenarios. In this work, we present a pioneering effort to investigate the capability of LLMs in transcribing speech in multi-talker environments, following versatile instructions related to multi-talker automatic speech recognition (ASR), target talker ASR, and ASR based on specific talker attributes such as sex, occurrence order, language, and keyword spoken. Our approach utilizes WavLM and Whisper encoder to extract multi-faceted speech representations that are sensitive to speaker characteristics and semantic context. These representations are then fed into an LLM fine-tuned using LoRA, enabling the capabilities for speech comprehension and transcription. Comprehensive experiments reveal the promising performance of our proposed system, MT-LLM, in cocktail party scenarios, highlighting the potential of LLM to handle speech-related tasks based on user instructions in such complex settings. The code, model, and samples are available at https://github.com/cuhealthybrains/MT-LLM.