Bashir is being held under tight security in solitary confinement, a source at the prison said.
Since his removal by the military last Thursday, Bashir had been detained under heavy guard in the presidential residence inside the compound that also houses the Defence Ministry, the family sources said.
The military ousted Bashir after weeks of protests against him that culminated in a sit-in outside the Defence Ministry compound that began on April 6.
Protests are still going on in spite his removal.
Awad Auf, who announced Bashir’s removal and said he was being detained in a “safe place”, stepped down as head of the ruling Transitional Military Council after only a day in the post.
Abdel-Fattah al-Burhan now heads the council, which has promised to hold elections within two years.