Messages/emails to dashboard

I’m building a site that is an intranet site that has no access to a mailserver, so I’m trying to learn if there is a way to still get visitor messages to the site admin.

Since there is no mailserver that it can interact with, I can rule out delivering messages to the admin’s email address. The alternative, as I see it, is to have the messages deliver to the dashboard. In a sense, it would be contact form to dashboard.

I did Google this idea without any luck. Thank you.