Al Jazeera'a Hiba Morgan, reporting from Khartoum, said officials disputed the report that al-Bashir was being held in the prison.
The coup team led by Defence Minister Awad Ibn Auf had indicated that al-Bashir was under arrest and was being kept in a safe place.
Several vehicles carrying paramilitary forces deployed on a bridge that connects the protest site with north Khartoum, a witness said.
Sudan has taken heavy losses in the unpopular war but grew heavily dependent in the last years of Bashir's rule on credit from the oil-rich Gulf Arab states to prop up the collapsing economy.
Witnesses said the army displayed a banner on one of the walls of their building facing the protesters.
Siddiq also called for the "immediate reform" of Sudan's National Intelligence and Security Service (NISS).
"We are now embarking on preparing the final list and putting the final touches for declaring the civilian government and the supreme council of state", said Sati' Al-Haj, spokesman of the National Consensus Forces, part of the Freedom and Change Alliance, on Tuesday.
Notre-Dame Cathedral Is Burning
Historian Camille Pascal spoke to French broadcaster BFMTV, saying the fire was destroying "invaluable heritage". He pledged to rebuild the church and said he would seek global help to do so.
"If our demand for the formation of a civilian transitional council with military representation is not met, we will not be part of the executive authority, the cabinet, and we will continue the mass escalation and the sit-ins to fulfill our demands", Ahmed al-Rabie, an SPA member, said.
"As the Troika of the United States, United Kingdom and Norway said on 14 April: 'To date, the legitimate change that the Sudanese people are demanding has not been achieved".
Bashir became in 2009 the first world sitting leader to be indicted by the ICC for war crimes committed in the years-long Darfur conflict, in western Sudan.
Following his deposition, al-Bashir was arrested, Lt. Gen. Abdel Fattah al-Burhan said.
"If Omar al-Bashir applies for asylum in Uganda that is a matter that can be considered by the president of Uganda", Uganda's Foreign Affairs Minister Henry Okello Oryem told reporters following a meeting in parliament.
Oryem said al-Bashir had yet to contact Kampala for possible refuge, but added that there was no harm in considering the fallen Sudanese leader for political asylum.
In The Hague, an International Criminal Court spokesman declined comment "on hypothetical situations".
As an ICC member, Uganda would have to hand over Mr Bashir if he arrived in the country.
The head of the TMC's political committee, Omar Zain al-Abideen, said on Friday the council would not extradite Bashir for trial, suggesting he could be tried in Sudan instead. Ugandan President Yoweri Museveni has repeatedly criticized the ICC, saying it unfairly targets Africans.