User profiling is the process of collecting information about a user in order to construct their profile. The information in a user profile may include various attributes of a user such as geographical location, academic and professional background, membership in groups, interests, preferences, opinions, etc. Big data techniques enable collecting accurate and rich information for user profiles, in particular due to their ability to process unstructured as well as structured information in high volumes from multiple sources. Accurate and rich user profiles are important for applications such as recommender systems, which try to predict elements that a user has not yet considered but may find useful. The information contained in user profiles is personal and thus there are privacy issues related to user profiling. In this position paper, we discuss user profiling with big data techniques and the associated privacy challenges. We also discuss the ongoing EU-funded EEXCESS project as a concrete example of constructing user profiles with big data techniques and the approaches being considered for preserving user privacy.