Google is sending out notifications to webmasters if they are running TLS 1.1 or lower. The notification isn't that Google search will rank the site lower or delist the site but rather Chrome, Google's browser will show a "not secure" warning to users if the site is running anything less than TLS 1.2.
It isn't new that Google Search Console is sending out notices for TLS issues, Google has been doing so since 2017.
Here is what the new one looks like from Barry Adams on Twitter:
Here is what it says:
Starting January 2020, Chrome (version 79) will show a "NOT SECURE" warning for all sites that don’t support TLS 1.2 or higher. In March 2020, Chrome (version 81) will show a full page warning message for these sites. Enable TLS 1.2 or higher on your site to help protect users' data and avoid triggering the new warning.
Some are saying that their sites are on TLS 1.2 and the notice is incorrect. There is a Google Webmaster Help thread with these complaints.
In any event, yes, you should upgrade to TLS 1.2.
Forum discussion at Google Webmaster Help and Twitter.
Update: Google confirmed some of the errors:
We recently sent out a small batch of messages to websites about TLS 1.0 / 1.1 support in Chrome. You can read more about the change at https://t.co/zjCYFqGOyX . While most of the messages were correctly sent to sites that have this issue, there were some false positives.
— Google Webmasters (@googlewmc) January 17, 2020
We're sorry for the confusion this message may have caused sites that are already using modern security configurations. Here's to a more secure & modern web!
— Google Webmasters (@googlewmc) January 17, 2020