Prompt engineering has made significant contributions to the era of large language models, yet its effectiveness depends on the skills of a prompt author. This paper introduces $\textit{iPrOp}$, a novel interactive prompt optimization approach, to bridge manual prompt engineering and automatic prompt optimization while offering users the flexibility to assess evolving prompts. We aim to provide users with task-specific guidance to enhance human engagement in the optimization process, which is structured through prompt variations, informative instances, predictions generated by large language models along with their corresponding explanations, and relevant performance metrics. This approach empowers users to choose and further refine the prompts based on their individual preferences and needs. It can not only assist non-technical domain experts in generating optimal prompts tailored to their specific tasks or domains, but also enable to study the intrinsic parameters that influence the performance of prompt optimization. The evaluation shows that our approach has the capability to generate improved prompts, leading to enhanced task performance.