Collaborative search engines (CSE) are an upcoming trend in WWW search. CSE let knowledge workers concert their efforts and support user collaboration. However, search terms and links clicked that are shared among users reveal their interests, habits, social relations and intentions. Thus, CSE might put the privacy of the users at risk. In this paper, we describe our first steps towards discovering the scope of privacy needs in CSE. We identify common components of CSE, and we describe typical use cases and user groups. Based on these information, we explore the range of privacy threats that might arise from query and link sharing. Furthermore, we outline a conceptual framework to explore the privacy needs of CSE users. Finally, we describe two findings from preliminary study results: First, our participants were less concerned about what providers might learn, but wanted to restrict information disclosed to people in their social network. Second, we have identified a new class of reciprocal privacy preferences, which allow or prohibit information disclose depending on the behavior of others.