Yu Suzuki strongly wants the games to be remastered to let Shenmue newcomers play the original two games and be prepared for Shenmue III. It would also preserve the Shenmue series and make it more accessible because not all gamers had Dreamcasts and Xboxs, or want to tinker with emulation.
However, it is mainly up to Sega, not Yu Suzuki. If it is made, then it will likely come out in 2018 before Shenmue III releases.
In 2016, a SEGA spokesman said they are currently investigating how to make it a reality, but the issue is primarily with the licensing in the original games.
Later, in September 2016, Sega Europe registered two domains "shenmuehd.com" and "shenmueremastered.com". It is unknown if these were done because an official project is underway, or simply to take these domain names in advance in case it was.