There's still no word from Square Enix on when Dragon Quest X's beta test will begin. But we do know when the first beta testers will be selected.
Square Enix announced today that applicants who were selected for the first round of beta testing will be notified on January 31. The application process began on November 16.
If you don't make it into the first round, you may still make it into future rounds.
Square Enix has not said future rounds will be selected. However, applications are still being accepted, so interested parties should visit the official site.