Queen's drummer Roger Taylor said that Whishaw is at the top of the band's wish list. Sacha Baron Cohen was originally attached to the part, but left the project over creative differences.
Graham King, Tim Headington, Robert De Niro and Jane Rosenthal will produce the film alongside Queen Films.
Playwright and screenwriter Morgan was nominated for a Drama Desk for his 2007 drama Frost/Nixon. He was Oscar-nominated for his screenplays of "Frost/Nixon" and "The Queen."