The 46-year-old has won rave reviews for her performance as therapist Linda, who cares for her sick daughter, in the dark comedy thriller and she feels "grateful" to have been given the chance to show off a new side to her work.
Discussing the Oscar speculation, Byrne told USA Today newspaper: "It's so flattering. I feel very emotional about it.
"I've been doing this a long time, so I feel grateful to have had such an incredible opportunity with this character."
The Bridesmaids actress pushed the humour in the movie to "lengths that (she has) never played before".
She added: "It's obviously very dark and very dramatic, this film. And there's elements of horror and Lynchian elements. It defies genre in many ways, which is really exciting, but this is definitely a tightrope."
Byrne surprisingly selected The Godfather star Robert De Niro as her favourite comedic actor.
She admitted: "That's obviously not something maybe necessarily people would say at the top of their head.
"(But) look at him, he's so funny in his intensity."
The Spy star thinks her background has helped her to establish herself in the comedy world.
She said: "Culturally Australians are very much bred to not take ourselves too seriously but to take the work seriously."
And putting a darker spin on things comes naturally to Byrne.
She quipped: "Gosh, isn't that just waking up? I just think that's life. I don't even know how funny it is, to be honest, but it's real dark."
One of Byrne's favourite scenes in If I Had Legs I'd Kick You centres around a hamster, who Linda buys as a pet for her daughter, only for it to escape on the journey home, meeting a gruesome end in the street when it jumps out of the car.
She laughed: "On the page, the hamster is described as Jack Nicholson from The Shining trying to scratch through the door. And I fell apart.
"It's absurd and that's what we had to capture. ... You're thinking, 'Don't do it. Don't get the hamster. Oh, no, she got the hamster.' It's like this doom, just this ominous thing of 'Oh, God …' "
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