Bradley Cooper is also nominated for his direction of and performance in the musical remake.
Olivia Colman is also up for a best actress award for The Favourite, for which Rachel Weisz and Emma Stone are also recognised.
Rosamund Pike is nominated for best actress in a film drama, alongside Lady Gaga, for her role in A Private War.
Colman, meanwhile, will compete for the best actress in a film musical or comedy award with Emily Blunt, shortlisted for playing the title role in Mary Poppins Returns.