Reports say the ex-leader has until now been detained at the presidential residence under heavy guard.
He is reportedly being held in solitary confinement and is surrounded by tight security.
Months of protests in Sudan led to the ousting and arrest of the long-time ruler on Thursday.
Uganda’s Minister for Foreign Affairs Henry Oryem Okello told Reuters news agency the country would consider offering the deposed leader asylum if he applied, despite an arrest warrant issued by the International Criminal Court (ICC).
As an ICC member, Uganda would have to hand over Mr Bashir if he arrived in the country. The ICC has not yet commented.
Until now, Mr Bashir’s whereabouts since his removal were unknown. The coup leader at the time, Awad Ibn Auf, said Mr Bashir was being detained in a “safe place”. He himself stood down soon afterwards.
Lt Gen Abdel Fattah Abdelrahman Burhan was then named as head of the transitional military council, to become Sudan’s third leader in as many days.
Demonstrators have vowed to stay on the streets until there is an immediate move to civilian rule.