Part of the college's phased development programme, the 'drama performance and referral facilities' will sit next to the RWCMD's existing purpose-built home in the grounds of Cardiff Castle.
The scheme is the latest high-profile building project to be backed by the 58-year-old National Conservatoire of Wales.
John McAslan and Partners has already designed and built a 400-seat music pavilion - known as the Anthony Hopkins Centre - for the college.
The closing date for registration is 21 March and it is hoped the new facility will open in September 2009.
For more details visit www.ted.europa.eu (OJEU 2007/S28-034075).