According to Gamerzines, a source has indicated that high definition ports of both Shenmue and Shenmue II are already finished and ready for release on Xbox Live Arcade and PlayStation Network.
"Shenmue HD is real [and has been] finished for well over a year. As is Shenmue II HD," they claimed.
According to the source, the reason Sega has not released either game yet is to plan whether it will continue the series with Shenmue III.
In the past Sega has said it has no plans for a third Shenmue game, but that fans should "never say never".
Series creator Yu Suzuki commented last year that he would like to make Shenmue III and that the concept for the sequel already exists.
Sega hinted earlier this week that Shenmue and Skies of Arcadia are the two most requested games for high definition remakes.
Watch the Dreamcast gameplay trailer for Shenmue below: