According to the Guardian newspaper, a female lawyer who claims to have been subjected to unwanted sexual advances by Mr Khan had raised concerns about the competence of the Independent Oversight Mechanism (IOM), the ICC's watchdog.
The paper also reported that Khan responded to a formal sexual misconduct complaint against him by trying to persuade the alleged victim that she should deny the claims, despite having been advised to avoid one-to-one contact.
Mr Khan denied asking the woman to withdraw any allegations, the Guardian reported.
Paivi Kaukoranta, the president of the body charged with overseeing the court, last month said the IOM had been in contact with the alleged victim, but said it was not in a position to proceed with an investigation at that stage.
In a statement on Monday, she defended the IOM's ability to carry out the investigation but said that "given the particular circumstances," she did not object to "exceptionally resorting to an external investigation".
"An external investigation is therefore being pursued in order to ensure a fully independent, impartial and fair process," she said.
It comes amid intense scrutiny of the ICC and Mr Khan after the prosecutor's request for arrest warrants linked to the conflict in Gaza.
In May, Mr Khan said there were reasonable grounds to believe that Israeli Prime Minister Benjamin Netanyahu and then-defence minister Yoav Gallant, and Hamas leaders Yahiya Sinwar, Mohammed Deif and Ismail Haniyeh bore criminal responsibility for war crimes and crimes against humanity from the day of Hamas's attack on Israel on 7 October onwards.
Sinwar, Deif and Haniyeh have all since been killed by Israel.
In an earlier statement, Mr Khan did not explicitly blame Israel, but did juxtapose the sexual misconduct allegations and efforts to undermine his position when he described this as "a moment in which myself and the International Criminal Court are subject to a wide range of attacks and threat".
But the sexual misconduct allegations are understood to pre-date his request for arrest warrants linked to the conflict in Gaza.
A panel of three ICC judges is currently considering the arrest warrants requested by Mr Khan.