F5 way to monitor SQL always on and determine which site is active

Hi guys, I am just trying to figure out if there is a way to monitor SQL Always On using F5.

Currently we have F5 GTM/LTM in place. The application flow is as follows:

SITE A ---> Client ---> Web Tier ---> App Tier ---> DB SQL

The SQL instance is not currently hosted on F5. Lets say if there is a Web and APP VIP failure at SITE A then GTM will do a automatic fail-over to SITE B and everything will work but lets say if there is SQL failure in SITE A how does GTM will fail-over entire system (WEB and App VIP) from SITE A To SITE B.

Our security policy does not currently allows cross site communication.