Rev Hassan Abduraheem and Rev Kuwa Shamal (pictured) asked earlier in the month to be taken to court or to be freed after they had been detained for months without formal charge.
The pair face their first trial hearing on Sunday according to the international anti-persecution charity Christian Solidarity Worldwide (CSW).
On Thursday, both men were reportedly moved to Al-Huda Prison, in North Omdurman.
Previously, they had been living in police holding cells which are usually used to keep suspected criminals for short periods of time, while the prosecutor investigates potential criminal charges.
The men are being investigated for national security crimes and have not been formally charged.
They were originally arrested in December 2015.
The men are accused of seven crimes including "waging war against the state" and "espionage".
CSW has been told the men "are held in a small room where sometimes up to 25 men are also detained."
Last year, Rev Yat Michael and Rev Peter Reith, who faced similar charges, were released in August 2015.
Mervyn Thomas, CSW's chief executive said: "We are deeply concerned to learn of the serious charges levelled against Reverend Hassan Abduraheem and Mr Abdulmonem Abdumawla simply for seeking to assist with medical expenses, and against Reverend Kuwa Shamal merely for being a Christian and a friend of Reverend Abduraheem.
"These innocent men now face the possibility of a death sentence on evidence that would not justify an arrest, let alone a conviction, given its paucity."
CSW has asked Sudan's government to provide a fair trial with full access to legal help and family.
