The ability to predict a user's information need would have wide-ranging implications, from saving time and effort to mitigating vocabulary gaps. We study how to interactively predict a user's information need by letting them select a pre-search context (e.g., a paragraph, sentence, or singe word) and specify an optional partial search intent (e.g., "how", "why", "applications", etc.). We examine how various generative language models can explicitly make this prediction by generating a question as well as how retrieval models can implicitly make this prediction by retrieving an answer. We find that this prediction process is possible in many cases and that user-provided partial search intent can help mitigate large pre-search contexts. We conclude that this framework is promising and suitable for real-world applications.