He was forced out of power a little over a week ago by the military on the back of massive protests.
Former Sudanese Defense Minister General Awad Ibn Auf, who has been under US sanctions since 2007, stepped down as TMC chief on Friday, making way for General Abdel Fattah al-Burhan, a career military officer.
The Reuters news agency reports that he is being held in the capital Khartoum at the Kobar maximum security prison.
Speaking for the first time since the removal of Bashir, 75, last Thursday, representatives of the Sudanese Professionals Association (SPA) said they would not co-operate with the ruling council unless their demands were met.
The Umma Party is led by Oxford-educated Sadiq al-Mahdi, who was prime minister twice during the 1960s and 1980s and was ousted by Bashir in 1989.
"We appeal to all to move immediately to the protest camp to protect the revolution and its gains", it said in a statement.
Officials in Riyadh and Abu Dhabi are hoping to assert their influence in post-Bashir Sudan to bring Khartoum closer to their geopolitical orbits of influence, and farther away from Turkey and Qatar-two countries that Sudan has grown close to in recent years. Demonstrators fear that the army, dominated by al-Bashir appointees, will cling to power or select one of its own to succeed him.
But the 55-member African Union stood by its longstanding opposition to all military coups, giving the military council just 15 days to hand over to civilian rule or face suspension from the body.
The country's interim leaders have made concessions, including firing prosecutor general Omer Ahmed Mohamed, but protests want guarantees of a transition to a transparent democracy.
Uganda would consider granting asylum to ousted Sudanese president Omar Al Bashir, who is wanted by the International Criminal Court (ICC), a state minister said on Tuesday. He allowed a referendum to be held that led to the creation of a separate country for the people of South Sudan, whose people had for decades alleged discrimination and marginalisation by the Arab North. In his final years as president he defied the court, visiting friendly nations including several ICC member states. Al Bashir, who came to power through a military coup in 1989, is the target of two worldwide arrest warrants for genocide - one in 2009 and one in 2010 - war crimes and crimes against humanity in the Darfur region between 2003 and 2008.
December 2018 was the ideal storm - Sudan's economy was in free fall, with every household affected by the spiralling cost of living.
When Ibn Auf announced Bashir's overthrow, he said the former president had been detained.
Henry Okello Oryem, Uganda's minister of state for global affairs, told the parliamentary committee on foreign affairs that the ousted leader is a guarantor to the South Sudan peace process.