The 17 year old was considered for the title role in the new blockbuster alongside Johnny Depp, Anne Hathaway and Helena Bonham Carter.
But Cobain, whose father was late Nirvana rocker Kurt Cobain, is said to have rejected the part to focus on her education.
A source tells British newspaper the Mail on Sunday, "Tim thought she would be perfect, but she wants to go to university. She's incredibly focused and sensible."
The film, in which newcomer Mia Wasikowska tackles the role of Alice, is due for release in March (10).