According to sources in the US who claim to have seen the documents, Cheryl is concerned that 15-year-old Meadow's mum Rebecca Soteros has a drinking problem.
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Late star Paul and his daughter Meadow (far right)
The mother and daughter are apparently both currently living in LA with Cheryl, who is a registered nurse.
Meadow's grandmother states in the documents that it will be "necessary and convenient" for her to be appointed guardian of Meadow.
She also mentions that the little girl stands to inherit "upward of $16million" – a figure much less than the $25million which was previously reported.
Paul left his entire estate to his daughter, who had moved to Santa Barbara three years ago from Hawaii to live with him.
He appointed his father, Paul William Walker, as executor of his will and requested his mother be Meadow's guardian. So if Cheryl's petition is accepted, it will be in accordance with the star's wishes.
It's no surprise that the star left his estate to his only child.
"He told me recently he was the happiest he'd ever been," Paul's close friend Brandon Birtell told People shortly after his death. "It was directly because of his growing relationship with his daughter and the clarity that brought to his life."