Setting the WP_HTTP_BLOCK_EXTERNAL constant to true in your wp-config.php file will stop all outgoing network requests from your site. This is typically set on sites that are sitting behind a closed environment.

However, having this set is problematic when performing migrations using WP Migrate DB Pro or allow updates for WordPress:

Using WP_ACCESSIBLE_HOSTS you can set allowed hosts like so:

define('WP_ACCESSIBLE_HOSTS', 'api.wordpress.org,nightshiftapps.com');