Addition of features such as internet access via wireless and other sophisticated functions have converted the present day mobile phone into smart devices with multiple applications. One such area is the educational sector, where several features of mobile phone come in handy. Mobile Learning or m-Learning is increasingly gaining importance among learners, educators, and institutions as a medium of education. In view of the ubiquitous nature of mobile technology and the immense opportunities it offers, there are favorable indications that the technology could be introduced as the next generation of learning platforms. M-learning platform however lacks a comprehensive assessment and evaluation methodology, which is hampers its implementation considering the rapidly changing technology. In this context this paper addresses the question: "Can the notion of the capability maturity model (CMM) be adapted to propose m-Learning maturity?". The basic idea is to consider and use the CMM framework as an inspiration to build a model appropriate for m-Learning that would help measure the maturity of educational institutions in adopting m-Learning. This is a preliminary discussion based on the current understanding of the issue.