Valve has announced that the beta testing for Linux Steam client will begin sometime this October. This testing will only be available to 1000 users and will be private. Currently the client is ready and undergoing internal beta testing.
The beta test will include only one game, which is hopefully Left For The Dead 2. Also only Ubuntu 12.04 and above will be supported in this release. Further some of Steam features like additional games and Big Picture Mode will not be available.
You can read the announcement here.