In a post on the Capcom Unity forums Christian Svensson, Capcom VP of strategic planning & business development, discussed the challenge with giving the HD Remix treatment to Street Fighter III: 3rd Strike.
An HD Remix on SF3 would be a challenge in and of itself given the number of frames of animation and effects that would have to be redone, especially in light of what we learned on SSF2THDR. As such, the very nature of the project you're suggesting is somewhat unlikely.
Personally, I would take a port. SF3 is a great fighting game that could find a whole new audience now that Street Fighter IV is out. I don't need an HD Remix for SF3. It still looks great. I'm also going to assume that a re-release of SF3 with multiplayer will happen, given Capcom's strategy for re-releasing its old 2D fighters.
Not familiar with 3rd Strike? It's the game that the infamous Daigo perfect parry comes from:
Svensson also confirms that, if a re-release were to happen, it would be downloadable and not a retail release.