Law has already won a Critics' Circle prize for his role as Hamlet
Jude Law, James McAvoy, Rachel Weisz and Keira Knightley are among the nominees for the prestigious Laurence Olivier theatre awards.
Law and McAvoy are up against James Earl Jones, Mark Rylance, Ken Stott and Samuel West in the best actor category.
Weisz, Juliet Stevenson and Imelda Staunton are among those nominated for best actress, while Knightley is up for best supporting actress.
The winners will be announced at a ceremony in London on 21 March.
Law's nomination comes for his leading role in Hamlet at the Wyndham's theatre in the West End.
McAvoy is recognised for his performance in Three Days Of Rain at the Apollo theatre.
Knightley is nominated for her turn in The Misanthrope at the Comedy Theatre.
Lucy Prebble's Enron and Jez Butterworth's Jerusalem have six nominations each, and go head-to-head in the best new play category.
Former Spice Girl Melanie C is amongst the nominees for best actress in a musical for her West End debut in the long-running musical Blood Brothers.
Rowan Atkinson is nominated as best actor in a musical for his role as Fagin in Oliver!
"The voting for the best acting awards was so close that the nominations had to be increased," said the president of the Society of London Theatre, Nica Burns.
The Royal Court theatre has a total of 15 nominations for four productions - Cock, Enron, Jerusalem and The Priory.
The Oliviers are presented by The Society of London Theatre to honour the best West End stage productions.
They were first held in 1976 and became known as the Olivier Awards in 1984 when actor Sir Laurence Olivier agreed to them being named after him.
The award winners are chosen by panels made up of members of the theatre-going public and theatre experts, apart from the Audience award, voted for solely by the public and presented to their favourite long-running London show.
This year's nominees are Billy Elliot, The Phantom of the Opera, War Horse, We Will Rock You and Wicked.
Gillian Anderson (Doll's House)
Lorraine Burroughs (The Mountaintop)
Imelda Staunton (Entertaining Mr Sloane)
Juliet Stevenson (Duet for One)
Rachel Weisz (A Streetcar Named Desire)
James Earl Jones (Cat on a Hot Tin Roof)
Jude Law (Hamlet)
James McAvoy (Three Days of Rain)
Mark Rylance (Jerusalem)
Ken Stott (A View From The Bridge)
Samuel West (Enron)
Best supporting actress
Hayley Atwell (A View From the Bridge)
Michelle Dockery (Burnt by the Sun)
Alexandra Gilbreath (Twelfth Night)
Keira Knightley (The Misanthrope)
Rachael Stirling (The Priory)
Ruth Wilson (A Streetcar Named Desire)
Best supporting actor
Mackenzie Crook (Jerusalem)
Rory Kinnear (Burnt by the Sun)
Tim Pigott-Smith (Enron)
Eddie Redmayne (Red)
Best new play