Architect GWP has designed the scheme to bring the grade II listed building, once frequented by Anthony Hopkins and Richard Burton, back to life.
If all the contractual agreements are concluded, full works on the cinema will commence later this year.
When it re-opens in 2021, the new cinema will have been converted into a multi-purpose community hub with recreational facilities, shops, and office space for local businesses.
Tim Chell, BAM’s director for Wales and the South West of England, said: “We’ve got an immensely strong record in Wales, where we’ve had a dedicated permanent office based in Cardiff since 1989.
“Our strength is our working style, which is highly collaborative, and we’re also known to be market leaders in technology.