The Nexus 6 for Verizon is seemingly being prepared for a September 12th update to Android 7.0 Nougat, according to Droid Life who points out that Verizon's support page for software updates details that the Google Nexus 6 shows that the device was "last updated" on September 12th of 2016. Since this coming Monday is September 12th, it looks like Verizon is preparing an update for the device following the weekend. Having said that, the support page does not list any details for the update other than the date itself, so it's also reasonable to assume that it may not be the update to Android 7.0 Nougat and it could instead be the update to the most recent Android Security Patch.
For now, there will be no way to know, so users of the Nexus 6 on Verizon's network will simply have to wait until Monday rolls around and Verizon starts pushing out the software that's dated for that time on their support page. As far as the unlocked Nexus 6, Google began pushing the Nougat update out to the Nexus 6 over-the-air back on September 6th which was just a few days ago. This was also alongside the OTA update to Android 7.0 Nougat for the Nexus 6P which went out at the same time, although it's only been a few days so it's possible that not all users on either device have the update just yet.
If it is Android 7.0 Nougat, Verizon Nexus 6 owners will be greeted with a stack of new changes to the software and interface as well as functionality, including things like the multi-window app use which will allow having two apps open on screen at any one time. Android 7.0 Nougat also further improves battery life by making improvements to Doze Mode, which will work while a phone is moving, say, in a pocket, instead of just when the device is stationary on a tablet, desk, or counter top. For those on a Verizon Nexus 6 patiently waiting to be bumped up to the latest Android software version, there's only a few more days to go until the possibility of moving off of Marshmallow arises.