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This paper presents our research on the feasibility of extracting Twitter users' interests for suggesting serendipitous connections using natural language processing (NLP) technology. Defined by Andel  as the art of making an unsought finding, serendipity has a positive role in scientific research and people's daily lives. Applications that facilitate serendipity would bring various benefits to us. In this work, we focus on the mining of users' interests from Twitter messages (tweets hereafter) to support the detection of serendipitous connections. To address the challenge, we explore a set of NLP tools to develop a real-time system for automatically extracting the users' interests in the form of named entities and core terms. We also examine the different contributions of three different information sources with regard to the user's interests. Furthermore, we examine the issue of determining the additional attribute of surprisingness/ unexpectedness of the terms and entities of interest which we deem critical for detecting serendipitous connections. Our prototype system was tested with a group of Twitter users involving approximately 2,300 tweets. Our algorithm achieved varying degrees of success on each of the users, demonstrating feasibility of identifying serendipitous interest terms and entities. For example, 27.5% of terms extracted for one of the users were judged to be serendipitous.