An information-theoretic mechanism for privacy-guaranteed interactions is introduced between two memoryless correlated sources where each source is characterized by a pair of public and private variables. The interactions are modeled as a collection of K/2 pairs of random mappings, one pair for each of the K rounds of interactions. The K/2 random mapping pairs are chosen jointly to minimize the information leakage (privacy measure) over K rounds of the private variable of each source at the other source while ensuring that a desired measure of utility (distortion) of the revealed public variable is satisfied. Arguing that an average case information-theoretic privacy metric can be appropriate for streaming data settings, this paper shows that in general, interaction reduces privacy leakage by drawing some parallels between this problem and the classic interactive source coding problem. Specifically, for the log-loss distortion metric it is shown that the resulting interaction problem is an analog of an interactive information bottleneck problem for which a one-shot interactive mechanism is, in general, not optimal. For the resulting problem with a non-convex constraint space, an algorithm that extends the one-way agglomerative information bottleneck algorithm to the interactive setting is introduced.