Gene expression profiling provides profound insights into molecular mechanisms, but its time-consuming and costly nature often presents significant challenges. In contrast, whole-slide hematoxylin and eosin (H&E) stained histological images are readily accessible and allow for detailed examinations of tissue structure and composition at the microscopic level. Recent advancements have utilized these histological images to predict spatially resolved gene expression profiles. However, state-of-the-art works treat gene expression prediction as a multi-output regression problem, where each gene is learned independently with its own weights, failing to capture the shared dependencies and co-expression patterns between genes. Besides, existing works can only predict gene expression values for genes seen during training, limiting their ability to generalize to new, unseen genes. To address the above limitations, this paper presents GeneQuery, which aims to solve this gene expression prediction task in a question-answering (QA) manner for better generality and flexibility. Specifically, GeneQuery takes gene-related texts as queries and whole-slide images as contexts and then predicts the queried gene expression values. With such a transformation, GeneQuery can implicitly estimate the gene distribution by introducing the gene random variable. Besides, the proposed GeneQuery consists of two architecture implementations, i.e., spot-aware GeneQuery for capturing patterns between images and gene-aware GeneQuery for capturing patterns between genes. Comprehensive experiments on spatial transcriptomics datasets show that the proposed GeneQuery outperforms existing state-of-the-art methods on known and unseen genes. More results also demonstrate that GeneQuery can potentially analyze the tissue structure.