Welcome to McAfee Communities. It sounds like you may have inadvertently picked up a (PUP) Potentially Unwanted Program. You may try running some of the Superb Free Tools Listed here:Anti-Spyware/Malware & Hijacker Tools I would try running McAfee Stinger (Read how to use). Follow up with Malwarebytes (Free) DO NOT accept or enable any Free Trial Offers/or activate the Paid/Pro Version.
Then I would follow up with AdwCleaner. Please apprise us if you need further assistance.
Should you feel the need to contact Technical Support (Free):Services and Support for Home and Office
All the very best
McAfee Community Moderator
Let's start with the basics.
The warning message looks like one of the SiteAdvisor messages. Have you got SiteAdvisor installed?
You say, "when I move about the internet". Does the message appear on every site, or only on some sites? Does it always appear if you go to this or that website, or is it more sporadic than that?
You've done scans and there's no malware present. So far so good. But it may be that something is running on your system that keeps connecting to a server somewhere and keeps trying to download a file that McAfee regards as dangerous. The first thing to do then is to use one or more junk-removal programs to clear out browser caches, temp files, cookies, anything irrelevant. Use QuickClean or CCleaner or Windows own Disk Cleanup. If there's a file which has been set running, maybe this will get rid of it. Then shut down and reboot. When Windows comes back up open Task Manager, or better use Process Explorer from Sysinternals, to look for any running program or process with an unusual name. Process Explorer lets you examine the properties of any running program so you can see if it's legitimate.
It's quite possible that what you're seeing is a download manager in operation. These can be the cause of a lot of unwanted programs, as they bundle unwanted stuff with some freebie that you did want. If you suspect you've got adware running on the system, you need to run both AdwCleaner (get it from BleepingComputer.com) and Malwarebytes. McAfee often won't flag adware and other Potentially Unwanted Programs; those other programs specialise in detecting them.
Try those for starters and let us know how you get on.