HTC hasn't built a Nexus phone in a very long time. They built the original, which I think has been the most solid Nexus phone yet, but surprisingly Google hasn't used their devices since, or perhaps HTC themselves didn't want to do it. If that's so then I think it was a big mistake, because when they made the Nexus One, HTC started being seen as a major Android player in the market, and it was loved not only by the media, but also the developer community, which in turn means a big portion of the users wanted it.
Perhaps what HTC needs right now to regain its strength in the smartphone market is just that - making a stock Android phone. Even better if that phone is "blessed" by Google, with all the free marketing HTC would get for making the upcoming Nexus phone. I think HTC still makes the best Android phones in the market, in terms of build quality, and the latest HTC One just reinforces that.
It's especially true now that they cracked the code for making full aluminum casings for their phones. Nothing is as solid or as premium-feeling as an aluminum phone. With a little help from Google, guiding them to what the specs for that Nexus phone should be, an HTC Nexus phone would make perfect sense this year. HTC needs it, and the users want it and would buy it. There have been quite a few voices from both the tech media and from regular consumers, requesting a HTC device with stock Android, ever since the HTC One X.
Making the Nexus 4 has been pretty great for LG, a company not many were willing to trust anymore after previous sub-par devices that they launched on the market. But thanks to the Nexus brand and Google's faith in them, that put LG a little more in media's crosshairs, and the users trust them a little more. Of course it's now up to LG to value that trust, and build on it, and keep making great devices, if they want the success to expand. I think the same thing would happen to HTC if they were to build the upcoming Nexus.
Also, this could be a very random thought, we may have already gotten a small confirmation that HTC may be building the next Nexus. Vic Gundotra said the next Nexus is going to have an insanely great camera, and I think he really meant it. It's not going to be just another run-of-the-mill camera that gets upgraded for this year. It's going to be something really different. Perhaps something like HTC's "ultrapixel" camera (which should be better even than Nokia's Lumia 920 in both picture quality and low-light performance), or at least something in that range.
Of course, there's also the possibility that someone else might've made a camera in that range - perhaps Sony, which would also be a pretty strong contender for the next Nexus. I doubt it's going to be Samsung, because first, I doubt the Galaxy S4 would offer such a camera (although Samsung may surprise us), and second, Google wouldn't use them for the 3rd time for a Nexus. But Sony also hasn't given us any signs that they are working on such cameras. If anything they are going to prolong that "megapixel myth" that HTC warned us about, and keep adding more MP to their cameras (without any pixel oversampling). On the other hand, neither has HTC.
It's also not going to be Motorola, because Google wants Motorola for their own X-phone (to be announced at Google I/O), and they wouldn't want to make their partners angry about it, either. So HTC still seems like the best choice for the next Nexus (for a fall launch), unless Google is very upset with HTC (for making WP8 phones perhaps?) or for some reason HTC still doesn't want to do it, but as mentioned above it would be a huge mistake on their part. HTC absolutely needs to make the next Nexus, because I'm not sure they can last another year, otherwise.
Reviewers are still mainly complaining about Sense, not necessarily the hardware of the latest HTC One, which seems like a pretty great all-around device, with little to no flaws. But Sense 5 doesn't really excite anyone. Stock Android on that phone would, which would bring some life even into HTC's other devices. There's no downside for HTC in this, and now they just need to make it happen, soon.