This app was mentioned in 3 comments, with an average of 2.67 upvotes
I use Drudge Report on Google Play. There is an option to get major headline notifications. A small IAP will turn off ads, as well. Highly recommended as there is a night mode, too!
Edit: Here is the link.
https://play.google.com/store/apps/details?id=com.iavian.dreport&hl=en
Drudge report not bad https://play.google.com/store/apps/details?id=com.iavian.dreport