Fake news, along with the speed of mass communication via social media, is having a significant impact on our social life, particularly in the political world. Fake news detection on social media has recently become an emerging research area that is attracting tremendous attention. Existing studies have proposed to employ traditional machine learning (ML) or emergent deep learning (DL) methods to detect fake news. These ML or DL methods based on batch processing and learning from a training dataset, however, are inefficient in conducting continual real-time fake news detection for incoming unseen social media data. In this research, we propose to use online machine learning (OML) to automatically identify fake news in real time. We investigated various online learning algorithms, including Approximate Large Margin Algorithm (ALMA), Passive-Aggressive (PA), etc., and compared their performance with some existing ML or DL methods for real-time fake news detection on Twitter. The preliminary results of our study demonstrate the considerable potential of OML techniques in classifying real-time fake news, thus highlighting the adaptability and robustness of OML in handling dynamic information streams such as fake news.