Director/producer Kevin Allen has obtained the movie rights to the 1954 work, which features the dreams and innermost thoughts of the inhabitants of a fictional Welsh fishing village, the Hollywood Reporter said.
Allen is planning to make back-to-back English and Welsh language versions of the project, which was previously tuned into a big screen release by filmmaker Andrew Sinclair in 1972.
Allen has cast 'Notting Hill' star Ifans in the role of First Voice, which was originated onscreen by Burton. Burton's on/off wife Dame Elizabeth Taylor also starred in the 1972 film.
Filming on 'Under Milk Wood' is due to begin this summer.