The police sources said Friday the men escaped from Khartoum’s Kober prison the night before.
Reuters newswire cites a police spokesman saying the men left using the prison’s drainage system.
The U.S. Embassy in Khartoum said it was looking into reports of the escape.
The four men, described during the trial as Islamist extremists, were convicted of shooting to death USAID official John Granville and his driver Abdel Rahman Abbas in Khartoum on New Year’s Day 2008.
The men said they were tortured into confessing to the murders.
All four were sentenced to hanging.
A fifth man found guilty of involvement in the killings received a lesser sentence of two years in prison.
Under Sudanese law, the families of murder victims can forgive the killer, seek compensation or demand the death penalty.
Abbas’s family had pardoned the accused, but the court confirmed this week that both Granville’s family in the U.S. and Abbas’s wife requested execution.
The judge emphasized that murders are illegal under both Sudanese and Islamic law, regardless of the nationality or religion of the person killed.
Some information for this report was provided by AFP and Reuters.