In a designated verifier signature (DVS) scheme, a signer (Alice) generates a signature which can only be verified by a designated verifier (Bob) chosen by her. Moreover, Bob cannot transfer his conviction about Alice’s signature to any third party. A DVS scheme provides the capability of authenticating Alice to Bob without disrupting her privacy. A multi designated verifier signature (MDVS) scheme is an extension of a DVS which consists of multiple designated verifiers. Non-delegatability is an essential property of a DVS scheme in scenarios where the responsibility of a signer (Alice) is important and she must not be able to delegate the signing rights to another entity. In this paper, we discuss on all MDVS schemes proposed up to now (to the best of our knowledge) and show that all of them are delegatable. As a result, proposing a non-delegatable MDVS scheme is an open research problem in the literature.