"following the news" is a correct and usable phrase in written English. You can use it to mean to be keeping up with current events or to learn about recent developments in a particular topic. For example, "I've been following the news about Brexit closely over the past few weeks."
I've been devoting all my time to following the news, anxiously delving into every new development.
Bank shares rose following the news.
He is following the news now.
Was she following the news reports?
But I'm not following the news.
Twitter's stock fell more than 4% following the news.
This suggests that Russians are not following the news.
Yet most Americans yawned – only 14% in a Gallup poll said they were following the news very closely, and 35% said they were following the news somewhat closely.
In recent weeks, you may have been following the news reports about the admissions lawsuit.
"People are following the news, wondering what's coming next," he said.
Steph Hoy has been following the news about the French fuel strike anxiously.
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia