The August: Osage County star has revealed she believes 23-year-old Jennifer Lawrence is too edgy to hold the unofficial title.
Julia previously admitted she always hated being put on a pedestal and being heralded as the most popular actress in Hollywood.
'People should understand that there is nothing tremendously unique about me. I have this tremendously unique job, but we are looking for the same thing, which is to be understood, honoured and loved. I hate the pedestal feeling, the fake heralding,' she said.
The Erin Brockovich star has moved away from the spotlight since starting a family - including eight-year-old twins Hazel and Phinnaeus and six-year-old son Henry - with 44-year-old husband Danny Moder.
She revealed that she no longer recognises her old self and prefers to spend most of her time with her family.
Jennifer was only 22 earlier this year when she won the Academy Award for Best Actress for her work in Silver Linings Playbook.
Julia was a 22-year-old young actress in 1990 when her hit film Pretty Woman with Richard Gere was released.