The developers behind Sega's remastered editions of Sonic the Hedgehog 1 and 2 are hoping that Sega will allow them to complete the trilogy by releasing their version of Sonic 3 & Knuckles for iPhone. Developers Christian Whitehead and Simon Thomley, also known as Taxman and Stealth, respectively, have voiced support for a fan-launched campaign to demonstrate interest in the project. The pair has previously developed remastered versions of Sonic CD, Sonic the Hedgehog, and Sonic the Hedgehog 2, all of which were published by Sega.

A prototype version of the game is already up and running, according to the Sonic 3 Remastered campaign site:

The duo now have an initial working version of a remastered Sonic the Hedgehog 3. The purpose of this site is to show Sega Networks that there is demand for this to be completed and released.

While a lack of interest on Sega's part my be preventing the release, it appears that there might also be a legal issue with part of the game's soundtrack. You can find more details about the campaign from the developers themselves at the links below.

Source: Sonic 3 Remastered, Simon Thomley