Lynn and Rick Bynes, who are applying for temporary conservatorship of their troubled 27-year-old daughter, are said to be concerned that Amanda's mental illness could lead to her causing herself physical harm if she is left without their supervision.
The pair's visit to court alongside their attorney Tamar Arminak comes after a judge extended Amanda's enforced stay at a psychiatric centre for a further two weeks as her mental state is evaluated.
Amanda's parents are said to be planning to citing various examples of their daughter's inability to look after herself as part of their argument that the actress should be released into their care. According to TMZ.com, Lynn and Rick will argue that their daughter is suffering from schizophrenia and needs 24/7 care.
While Amanda is said not to have accepted that she might have the condition, she is said to have acknowledged to her parents that she has moments when she is 'good Amanda', and others when she is 'bad Amanda'.
In order to convince the court to allow Lynn and Rick to take the actress into their care, they must prove she does not have the ability to provide for her own physical health (including food, clothing and shelter) and cannot make sound financial judgement.
Lynn and Rick will also have to prove they have a stable home for Amanda to reside - which will be their home in Thousand Oaks - and that there is no other realistic options to save their daughter than conservatorship.
Sources say her parents will highlight the gasoline fire incident in Thousand Oaks as evidence for her inability to protect herself from harm and refer to her mental illness to prove she cannot look after he savings.
Amanda allegedly used a canister of gasoline to fuel a fire outside an elderly woman's home near her parent's home in Thousand Oaks, California on Monday night.
Her pet dog was doused in gasoline during the incident, although was unharmed.
Amanda will not face criminal charges over the incident, as prosecutors judged her behaviour as that of a mentally ill person.
If the judge rules in their favour, TMZ claim the star's parents will petition to make the temporary conservatorship permanent, which would lead the judge to set a date for a fresh hearing and appoint Amanda a lawyer.
It had earlier been claimed doctors at her psychiatric centre have made an initial assessment that the actress is suffering from 'schizophrenic tendencies.'
According to reports, Bynes allegedly acts normally for up to ten hours at a time, but then becomes irrational and incoherent.
When learning that her pet dog was being cared for by her parents, the 27-year-old apparently became convinced they would harm it.
Her anxiety led to her suffering an episode in which she became so upset she had to be physically restrained.
A photo has also emerged showing the former Hairspray star hiding under a white sheet as she is wheeled between buildings by staff at the centre in Ventura, California.
Bynes has also been allocated her own room at the centre, after she allegedly began berating her room mate.
However despite her strange behaviour, Bynes has reportedly tested negative for all illegal drugs except marijuana.