Abstract: File catalogue size has a large impact on the performance of wireless edge caching. Based on the Zipf file popularity model, this paper analyzes the asymptotic relationship between the file catalogue size and the number of user requests and the popularity parameters. The analytical results show that, when the number of requests is small, the size of the file catalogue increases linearly with the number of requests, and when the number of requests is large, the size of the file catalogue increases in a negative exponential manner with the number of requests. The results are valid for different popularity parameters. The accuracy and validity of the obtained analytical results are verified by simulations and a real dataset for a typical video website collected in a campus network. In practical systems, the number of requests within the coverage of a wireless edge node is usually much smaller than the total number of files on a video website. Therefore, the size of the file catalogue increases linearly with the number of requests, rather than the sublinear growth conjectured in the literature. This poses a serious challenge for wireless edge caching.