The project would mark the Oscar-winning actor's directorial debut.
Writer Ronald Harwood is penning the script, based on his 1999 stage play of the same name, reports Screen Daily.
"Dustin's coming on board as the director is the icing on the cake, really," said Christine Langan, creative director of BBC Films.
She added: "His understanding of the material and his take on it is incredibly exciting, deep and inspiring."
Maggie Smith, Tom Courtenay and Albert Finney are in talks to star in the film about elderly opera singers living in a London retirement home.
Production is expected to start in the UK in autumn.