Search Tracking

Where would I be able to find a list of all of the searches performed in the search bar for individual websites? Is there a way that we can create an automated monthly report of this information?

Ideally we want to be able to use this information with our customers, letting them know how many people are searching for them on a monthly (or aggregate basis). Both for current customers and used in new business.

I'm running a multi-site network.

Please let me know, thank you!