Server as Service in background for Android?

I have a notification hanler, which manages to notifiy the user by means of various ways (Snachbar, NotificationManager).

I would like to enhace tihs functionality by adding a service to that notification manager, which runs always in the background and waits/listens for notifications from the backend.

When I trigger a message from my backend like "Please update your app from PlayStore" it should be shown to the user. (I know how to do this, when I triger that from the mobile by a REST call to my endoint.) But I dont know, if it is possible to listen (on a port or something) as a server?