Sentiment analysis is a major area of natural language processing (NLP) research, and its sub-area of sarcasm detection has received growing interest in the past decade. Many approaches have been proposed, from basic machine learning to multi-modal deep learning solutions, and progress has been made. Context has proven to be instrumental for sarcasm and many techniques that use context to identify sarcasm have emerged. However, no NLP research has focused on sarcasm-context detection as the main topic. Therefore, this paper proposes an approach for the automatic detection of sarcasm context, aiming to develop models that can correctly identify the contexts in which sarcasm may occur or is appropriate. Using an established dataset, MUStARD, multiple models are trained and benchmarked to find the best performer for sarcasm-context detection. This performer is proven to be an attention-based long short-term memory architecture that achieves an F1 score of 60.1. Furthermore, we tested the performance of this model on the SARC dataset and compared it with other results reported in the literature to better assess the effectiveness of this approach. Future directions of study are opened, with the prospect of developing a conversational agent that could identify and even respond to sarcasm.