The U.N.'s Office of Internal Oversight Services (OIOS), which is leading the inquiry, has started contacting witnesses, a source with direct knowledge of the investigation said.
Khan's office and lawyers did not immediately respond to requests for comment.
A diplomatic source, who also spoke on condition of anonymity to discuss a confidential investigation, said the court's governing body wanted the inquiry concluded quickly to limit its impact on several major cases before the Hague-based institution.
The ICC's governing body said last month that it would seek an external investigation into the allegations, "to ensure a fully independent, impartial and fair process".
The ICC is a permanent court that can prosecute individuals for war crimes, crimes against humanity, genocide and the crime of aggression in member states or by their nationals.
Khan noted in October when the allegations were first reported that his office had been the target of a "wide range of attacks and threats" that had coincided with several high-profile war crimes investigations.
Last month, the court issued arrest warrants for Israeli Prime Minister Benjamin Netanyahu and his former defence chief Yoav Gallant, accusing them of war crimes and crimes against humanity in the Gaza conflict. Israel rejects the allegations.
In 2023, the court ordered the arrest of Russian President Vladimir Putin and Maria Lvova-Belova, Russia's commissioner for children's rights, accusing them of the war crime of illegally deporting hundreds of children from Ukraine. They deny the allegations.
Several NGOs and members of the prosecutor's staff have urged Khan to step down during the inquiry to avoid it interfering with work by the office.
Asked about the news that he would be allowed to stay on, Alix Vuillemin who leads one of the NGO's that called for Khan to step aside told@ Reuters that her organisation - Women's Initiatives for Gender Justice - still believes "it would be most gracious" if Khan decided to temporarily step back.
The case involving Khan was initially referred to the ICC's oversight mechanism in May, but it said it would not proceed because the victim had not confirmed the allegations. No official investigation was opened at that time.
