Agile methods fit well for software development teams in the requirements elicitation activities. It has brought challenges to organizations in adopting the existing traditional methods, as well as new ones. Design Thinking has been used as a requirements elicitation technique and immersion in the process areas, which brings the client closer to the software project team and enables the creation of better projects. With the use of data triangulation, this paper brings a literature review that collected the challenges in software requirements elicitation in agile methodologies and the use of Design Thinking. The result gave way to a case study in a Brazilian public organization project, via user workshop questionnaire with 20 items, applied during the study, in order to identify the practice of Design Thinking in this context. We propose here an overview of 13 studied challenges, from which eight presented strong evidence of contribution (stakeholders involvement, requirements definition and validation, schedule, planning, requirement details and prioritization, and interdependence), three presented partial evidence of contribution and two were not eligible for conclusions (non-functional requirements, use of artifacts, and change of requirements). The main output of this work is to present an analysis of the use of Design Thinking to see if it fits properly to be used as a means of solving the challenges of elicitation of software requirements when using agile methods.