SEGA Europe has registered a Shenmue HD related domain name after picking up ShenmueHD.com (whois) late last year.
Currently, the domain returns a white screen. Looking at the source code of the page being displayed, the page is detecting browsers while loading scripts from Amazon Web Services (AWS).
SEGA has previously mentioned that it is “investigating” remasters of Shenmue and Shenmue II but nothing more. Yu Suzuki has also mentioned in a Twitch stream that he would be speaking with SEGA about making it happen. Whether SEGA is preemptively picking up the domain ahead of some kind of announcement or is just registering the domain to prevent anyone else doing it is unknown.
Shenmue III is currently being developed for PlayStation 4 and PC at Ys Net after meeting its funding goal on Kickstarter.