His second year of detention under an emergency law that allows the government to jail people without trial ends on Friday.
Turabi, a former head of parliament, was a long-time ally of President Omar al-Beshir until losing out in a power struggle in late 1999. He was jailed in February 2001 and then placed under house arrest six months later.
Sudan recently freed 32 political prisoners in what analysts said could be an attempt to broaden support for ongoing peace talks in Kenya with the southern rebel Sudan People’s Liberation Movement to end a 20-year-old civil war.
Bashir also promised to end media censorship and lift a state of emergency, in force since 1999, as soon as peace was achieved in Sudan, the newspaper said.
Turabi's party, the Popular Congress, meanwhile dismissed two presidential decrees which the authorities had touted as marking a loosening of their grip on political life.
The creation of a National Press Council to supervise the media merely transferred censorship powers from one government body to another, the party charged.
And a second decree issued on Tuesday cancelling a list of Sudanese barred from travelling abroad had little effect as the courts retained the authority to reimpose the travel bans, the party complained.