Google seems to be testing a form of messaging between businesses and merchants that use Google Merchant Center. Google said in an email to some Google Merchants that it is testing a "new messaging pilot to help you connect with customers and improve your sales through Google Shopping."
Kirk Williams shared the email on Twitter and the email goes on to explain that this is an "optional feature" that will "allow customers to send messages to the customer service email address you've provided in your Merchant Center account."
It seems like Google will let a customer message a merchant through Google Shopping and that message will be emailed to the merchant who can then reply to send that customer a message in return.
This is a pilot, which means you need to apply and then be approved. I do not have any links but maybe you can ask Kirk, here is the email:
Forum discussion at Twitter.
