Trust negotiation is a promising approach for establishing trust in open systems, where sensitive interactions may often occur between entities with no prior knowledge of each other. Although several proposals today exist of systems for the management of trust negotiations none of them addresses in a comprehensive way the problem of privacy preservation. Privacy is today one of the major concerns of users exchanging information through the Web and thus we believe that trust negotiation systems must effectively address privacy issues to be widely acceptable. For these reasons, in this paper we investigate privacy in the context of trust negotiations. More precisely, we propose a set of privacy preserving features to be included in any trust negotiation system, such as the support for the P3P standard, as well as different formats to encode credentials.