Is it possible to upload an app to Google Play and it's only available to a list of users I'm interested in?
As happens on YouTube you can only see that video who is allowed to view that link. I have the following situation, I need my app to be available to download for only a few users that I have released.
But I would not want to put this APK on a server outside of Google Play. Is there any way to do this?
Yes, as Lucas said, if you set up your application in alpha or beta phase, the app will not be visible to the public in google play.
To give access to a limited group of people, you can set up google + communities or google groups, of course people need to participate in order to access the app. All people are considered testers and may by accepting, downloading and updating the app from google play, as well as a user of any app.
The images below show how to configure this:
If you have a company or work for one and it is registered in Google Apps for Business this is also possible and the way it is designed for this. The name is called Private Channel on Google Play.
Reference: Google Play Private Channel
