There isn't any support for S3TC texture compression support within Mesa / Gallium3D itself since it's covered by patents that don't expire for several years. Every time it seems there's good news to share on opening up S3TC, there isn't. Past talk of the patent being potentially invalid, etc, all haven't panned out. Yet every few months, optimistic independent developers think they have come up with a solution.
A German developer, Uwe Schmidt, started a new Mesa development thread entitled Another Take on the S3TC issue. In there he proposes a change to Mesa for different handling of S3TC types. With numerous Mesa developers already having invested significant amount of time into the S3TC issue, the idea wasn't new and was quickly shot down. In response, "It's all patented...Until S3 grants it's IP to OIN or the patents expire, this is going to be the situation. We've been through this mental exercise of the last 5 years more times than I can count, and we always come back to the same place."
Those users of the open-source Mesa / Gallium3D Linux graphics drivers either need to rely upon the external Mesa S3TC library that is technically in violation of the S3TC patent or try using the S2TC library. Eventually ETC2, ASTC, and/or other texture compression methods will be devised that are more open-source friendly, but still for years to come there will be existing S3TC-dependent games/applications to support.