The metaverse is a nascent concept that envisions a virtual universe, a collaborative space where individuals can interact, create, and participate in a wide range of activities. Privacy in the metaverse is a critical concern as the concept evolves and immersive virtual experiences become more prevalent. The metaverse privacy problem refers to the challenges and concerns surrounding the privacy of personal information and data within Virtual Reality (VR) environments as the concept of a shared VR space becomes more accessible. Metaverse will harness advancements from various technologies such as Artificial Intelligence (AI), Extended Reality (XR), Mixed Reality (MR), and 5G/6G-based communication to provide personalized and immersive services to its users. Moreover, to enable more personalized experiences, the metaverse relies on the collection of fine-grained user data that leads to various privacy issues. Therefore, before the potential of the metaverse can be fully realized, privacy concerns related to personal information and data within VR environments must be addressed. This includes safeguarding users' control over their data, ensuring the security of their personal information, and protecting in-world actions and interactions from unauthorized sharing. In this paper, we explore various privacy challenges that future metaverses are expected to face, given their reliance on AI for tracking users, creating XR and MR experiences, and facilitating interactions. Moreover, we thoroughly analyze technical solutions such as differential privacy, Homomorphic Encryption (HE), and Federated Learning (FL) and discuss related sociotechnical issues regarding privacy.