Data visualization designers and clients need to communicate effectively with each other to achieve a successful project. Unlike a personal or solo project, working with a client introduces a layer of complexity to the process. Client and designer might have different ideas about what is an acceptable solution that would satisfy the goals and constraints of the project. Thus, the client-designer relationship is an important part of the design process. To better understand the relationship, we conducted an interview study with 12 data visualization designers. We develop a model of a client-designer project space consisting of three aspects: surfacing project goals, agreeing on resource allocation, and creating a successful design. For each aspect, designer and client have their own mental model of how they envision the project. Disagreements between these models can be resolved by negotiation that brings them closer to alignment. We identified three main negotiation strategies to navigate the project space: 1) expanding the project space to consider more potential options, 2) constraining the project space to narrow in on the boundaries, and 3) shifting the project space to different options. We discuss client-designer collaboration as a negotiated relationship, with opportunities and challenges for each side. We suggest ways to mitigate challenges to avoid friction from developing into conflict.