Mr al-Bashir has been in power for 30 years and been a hugely divisive figure since becoming president in 1989.
The minister of production and economic resources in North Darfur Adel Mahjoub Hussein confirmed consultations are under way to set up a transitional council to run the country.
Mr Hussein told Dubai-based al-Hadath TV that “there are consultations to form a military council to take over power after President Bashir stepped down”.
The announcement comes as Sudan’s armed forces were deployed in the capital of Khartoum amid reports of a coup against the leader.
The military were present on major roads and bridges in Khartoum as thousands of people flocked to an anti-government protest outside the ministry.
Tens of thousands of people marched through the centre of the capital Khartoum in jubilation, dancing and chanting anti-Bashir slogans.
MORE TO FOLLOW