Al-Bashir's fate has continued to look bleak since the military ousted him following protests by citizens who were disillusioned by his reign.
In an interview with state TV, al-Burhan also confirmed that former President Omar al-Bashir and senior officials from his entourage had been jailed.
At a sit-in outside Sudan's Ministry of Defence that began on April 6, protesters, who slept on the pavement, stood besides posters of Bashir that called on the ICC to put him on trial.
They accused it of being composed of "remnants" of Mr Bashir's regime.
Sacks stuffed with millions euros, Sudanese pounds and thousands of dollars were allegedly found at Omar al-Bashir's villa, a source in the East African country's judiciary said.
The military on Sunday said it was committed to giving power to the people and would consider a joint military-civilian council.
Ukraine quiet ahead of presidential election Since no candidate surpassed 50% threshold, the nation's next president will be chosen in a runoff scheduled for April 21. He also signed an association agreement with the European Union and secured visa-free travel for Ukrainians to the EU.
Lead activists in Sudan, the Sudanese Professionals Association (SPA) on Saturday postponed a planned announcement of a civilian-led transitional team. He said the military is considering the protesters' demands for a civilian council with a military representative.
"During these talks we've felt that the military council has no desire to hand over power", Rabia said.
There have been no images of the former president in prison, nor any response from the generals over a demand they give up power to a civilian administration.
An SPA spokesman previously told the BBC that the group "completely rejected" the transitional military council leading the country, and said protesters seek the dismantling of state intelligence agencies and the "full dissolution of the deep state".
As much as six million euros, five million Sudanese pounds and $351,000 is claimed to have been in the villa.
But despite moves to hold Mr Bashir and others to account, Sudan's army does not appear to have the confidence of protesters demanding civilian rule, BBC Africa correspondent, Alastair Leithead, says.
Separately, a source in Bashir's National Congress Party said authorities arrested the acting party head Ahmed Haroun, former first vice president Ali Osman Taha, former Bashir aide Awad al-Jaz, the secretary general of the Islamic movement Al-Zubair Ahmed Hassan and former parliament speaker Ahmed Ibrahim al-Taher.