Is there any extension out there which will send email notification when any core or module updates are available?
Is there a setting within magento which would allow us to receive email notification for core and module updates?
On Magento 1 you'll see the notification on the yellow bar at the dashboard. Also, with Magento2 works in a versy similar way.
Magento doesn't work as separated modules with different versions and publish dates for each module.
Normally when a new version is published (most or several of the core modules were updated) you'll get the notification about the new Magento version.
Also, you can subscribe to Magento newsletters to get email notifications about new versions, secutiry patches, etc.