Facebook login for pre-existing members only

Hi,

I have a multisite subsite that is private so that only registered users (as added by an admin) of that blog can access it.

I would like to know how easy it would be for those users to be able to login using Facebook or Google but to not allow anyone from logging in who is not already registered user. I guess it would be a case of blocking access if the email addresses on the social account and the wp account do not match.

Has anyone come across a plugin that would do this?

Many thanks