This paper proposes a novel automatic speech recognition (ASR) system that can transcribe individual speaker's speech while identifying whether they are target or non-target speakers from multi-talker overlapped speech. Target-speaker ASR systems are a promising way to only transcribe a target speaker's speech by enrolling the target speaker's information. However, in conversational ASR applications, transcribing both the target speaker's speech and non-target speakers' ones is often required to understand interactive information. To naturally consider both target and non-target speakers in a single ASR model, our idea is to extend autoregressive modeling-based multi-talker ASR systems to utilize the enrollment speech of the target speaker. Our proposed ASR is performed by recursively generating both textual tokens and tokens that represent target or non-target speakers. Our experiments demonstrate the effectiveness of our proposed method.