Remotely monitoring a patient's condition is a serious issue and must be addressed. Remote health monitoring systems (RHMS) in telemedicine refers to resources, strategies, methods and installations that enable doctors or other medical professionals to work remotely to consult, diagnose and treat patients. The goal of RHMS is to provide timely medical services at remote areas through telecommunication technologies. Through major advancements in technology, particularly in wireless networking, cloud computing and data storage, RHMS is becoming a feasible aspect of modern medicine. RHMS for the prioritisation of patients with multiple chronic diseases (MCDs) plays an important role in sustainably providing high-quality healthcare services. Further investigations are required to highlight the limitations of the prioritisation of patients with MCDs over a telemedicine environment. This study introduces a comprehensive and inclusive review on the prioritisation of patients with MCDs in telemedicine applications. Furthermore, it presents the challenges and open issues regarding patient prioritisation in telemedicine. The findings of this study are as follows: (1) The limitations and problems of existing patients' prioritisation with MCDs are presented and emphasised. (2) Based on the analysis of the academic literature, an accurate solution for remote prioritisation in a large scale of patients with MCDs was not presented. (3) There is an essential need to produce a new multiple-criteria decision-making theory to address the current problems in the prioritisation of patients with MCDs.