NT Coroner Elisabeth Armitage has been probing the death of Mr Walker in an inquest since September 2022.
Mr Rolfe shot the 19-year-old three times while on duty in the remote community of Yuendumu, though was acquitted of murder in a high-profile five-week trial last year.
Mr Rolfe's lawyer, Luke Officer, filed the submission two weeks out from his first appearance at the inquest.
His submission invites the coroner to "consider recusing herself from the inquest on the grounds of apprehended bias".
Responses to the submissions are to be filed by Friday and Mr Rolfe will have until Tuesday to file any reply.
The coroner will deliver a ruling by the end of the week.
The inquest into the Warlpiri man's death has been repeatedly disrupted by legal stoushes about whether Mr Rolfe and another officer have the legal right to refuse to provide evidence to the coroner.
Ms Armitage previously determined that witnesses could not decline to answer questions by invoking the penalty privilege, which Mr Rolfe did when he first appeared at the inquest in November.
The coroner's ruling was initially upheld by the NT Supreme Court and was reaffirmed by the Court of Appeal.
It found that the continued operation of penalty privilege would contradict or diminish the operation of coronial legislation.
Mr Rolfe's legal team argued the coroner could not protect him from potential disciplinary action stemming from his evidence and the penalty privilege protections remained available to him as a common law right.
The ruling meant Judge Armitage could now be able to compel Rolfe to answer questions about racist text messages that the inquest was told he sent.
He is also likely to be asked about the night he killed Mr Walker, his previous alleged misuse of police body-worn cameras, previous alleged excessive use of force and an allegedly falsified NT police recruitment application.
Mr Rolfe was sacked from NT Police in April, after publishing a letter on Facebook, criticising the force and its commissioner for how they handled the inquest into the shooting.
The inquest is due to resume on October 23 but will not wrap up until at least March next year.
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