The COVID-19 outbreak was announced as a global pandemic by the World Health Organisation in March 2020 and has affected a growing number of people in the past few weeks. In this context, advanced artificial intelligence techniques are brought to the fore in responding to fight against and reduce the impact of this global health crisis. In this study, we focus on developing some potential use-cases of intelligent speech analysis for COVID-19 diagnosed patients. In particular, by analysing speech recordings from these patients, we construct audio-only-based models to automatically categorise the health state of patients from four aspects, including the severity of illness, sleep quality, fatigue, and anxiety. For this purpose, two established acoustic feature sets and support vector machines are utilised. Our experiments show that an average accuracy of .69 obtained estimating the severity of illness, which is derived from the number of days in hospitalisation. We hope that this study can foster an extremely fast, low-cost, and convenient way to automatically detect the COVID-19 disease.