In the context of End-to-End testing of web applications, automated exploration techniques (a.k.a. crawling) are widely used to infer state-based models of the site under test. These models, in which states represent features of the web application and transitions represent reachability relationships, can be used for several model-based testing tasks, such as test case generation. However, current exploration techniques often lead to models containing many near-duplicate states, i.e., states representing slightly different pages that are in fact instances of the same feature. This has a negative impact on the subsequent model-based testing tasks, adversely affecting, for example, size, running time, and achieved coverage of generated test suites. As a web page can be naturally represented by its tree-structured DOM representation, we propose a novel near-duplicate detection technique to improve the model inference of web applications, based on Tree Kernel (TK) functions. TKs are a class of functions that compute similarity between tree-structured objects, largely investigated and successfully applied in the Natural Language Processing domain. To evaluate the capability of the proposed approach in detecting near-duplicate web pages, we conducted preliminary classification experiments on a freely-available massive dataset of about 100k manually annotated web page pairs. We compared the classification performance of the proposed approach with other state-of-the-art near-duplicate detection techniques. Preliminary results show that our approach performs better than state-of-the-art techniques in the near-duplicate detection classification task. These promising results show that TKs can be applied to near-duplicate detection in the context of web application model inference, and motivate further research in this direction.