Independent Commissioner Against Corruption Michael Riches says he's considering the matter after Constable Zachary Rolfe was on Friday found not guilty of murdering Kumanjayi Walker on November 9, 2019.
"I am presently considering whether I should inquire into the circumstances of the investigation and arrest of Mr Rolfe," the commissioner said in a statement on Wednesday.
"While I appreciate the public interest in the matter I will not be rushed to decide whether or not I will investigate."
Const Rolfe, 30, was charged with murder four days after he shot Mr Walker, 19, three times during a failed arrest attempt in the remote Indigenous community of Yuendumu, 290km northwest of Alice Springs.
In wake of the trial, the constable's lawyer David Edwardson QC, the NT Opposition Leader Lia Finocchiaro and NT Police Association president Paul McCue have been critical of the investigation and the decision to lay charges against Const Rolfe.
Ms Finocchiaro and Mr McCue have also called for an independent inquiry.
They have also accused Chief Minister Michael Gunner of appearing to politically interfere in the investigation, which he has strongly denied.
Mr Riches' predecessor Ken Fleming QC stepped aside from an ICAC investigation into the shooting after a complaint was made about his comments at a protest in Alice Springs over the incident.
"I am aware of previous statements by this office relating to the ICAC's involvement in the NT Police investigation and ultimate arrest of Mr Rolfe," Mr Riches said.
"I am not aware of any investigative steps taken by the Office of the ICAC between 15 November 2019 and my commencement on 6 July 2021.
"Given the prosecution was already well underway when I started (the role in July 2021) I did not consider it appropriate to conduct inquiries at that time."
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