Valve has announced they will be testing internally their new Valve for Linux starting next week and a private external beta will be available sometime in October.
The external beta will only be available for 1000 users who will be provided with a sign up page that will be announced in a future post:
For existing Linux users, the external private beta is a good release for seeing where we are in running our games on Linux. We will be using a sign up page for the external beta. Information about the sign up will be announced in a future post.
The external beta will only include one game, which will probably be Left 4 Dead 2, although the post doesn't mention the game name. No additional Valve games will be included in the external beta and there will be no Big Picture mode. They also mention that only Ubuntu 12.04 and above will be supported.
Update: Steam For Linux Now Available To All Users