Family members said the former parliamentary speaker continued to be in custody, although the authorities did not formally order the renewal of his detention.
"He is still under house arrest," a family member said.
"There was no order to keep him there nor to release him," he added.
Turabi's arrest in February 2001 capped a power struggle with President Omar al-Beshir, who sacked him from his powerful post of parliamentary speaker in December 1999.
Turabi has been in detention since August 2002 under an emergency law that allows the government to detain people without pressing charges for a renewable period of one year.
His second year of detention under the law ended on Friday.
Though held in prison initially, Turabi is currently being held in a government detention home in capital Khartoum's Kafouri suburb.