According to series creator Yu Suzuki, a Shenmue and Shenmue 2 HD remake could be on its way. But it all depends on how Sega reacts to his proposition.
The acclaimed game designer recently took part in a Q&A session on Twitch, during which he addressed the possibility of updating the games. Suzuki was quick to reiterate that Sega holds the rights to Shenmue, so whether the remakes go ahead is up to them.
The developer is currently raising funds for Shenmue 3 on Kickstarter, with the game's record-breaking campaign passing $3.7 million as of this article. Suzuki also confirmed during the Q&A that he would like to release physical copies of Shenmue 3 on PS4, and is exploring how viable this is. He added that a demo for the game may be released ahead of its completion in 2017, and announced Kickstarter stretch goals up to $11 million. You can check all of Shenmue 3 reached goals and future goals on the Shenmue 3 Kickstarter page.