Private Messaging with page title as subject

I am wondering if the private messaging would be able to achieve the following scenario.

This is a woocommerce site and customers are browsing the site. He is interested in one of the listed item. Can the customer able to click on an icon and send a message to the site or product owner asking further questions? And the subject of the message will have the product page title included automatically so that the product owner knows what the customer is referring to?

Thank you.