Haneef would be questioned for the remaining 12 hours and released, unless they decided to charge him, added the spokesman.
The Australian newspaper said on Friday that despite questioning Haneef for 11 days, police had failed to find any evidence linking him to the British attacks.
Haneef, 27, is one of six doctors that have been questioned in Australia over the bombing plot which police have said is suspected of having links to al-Qaeda. The others have been released.
The Indian national who emigrated to Australia from Britain last year is a relative of Kafeel and Sabeel Ahmed, two suspects being held in Britain.
Two car bombs primed to explode were discovered in central London early on June 29, and the following day a jeep crashed into the terminal building at Glasgow airport and burst into flames.
Haneef was arrested in the eastern Australian city of Brisbane on July 2 while trying to leave the country on a one-way ticket to India.
Civil rights groups and lawyers have called for Haneef to either be charged or set free.
On Friday, John Howard, the Australian prime minister, defended Haneef’s detention without charge.
“I’m happy with the laws because I sponsored them. I defend them. We do need to arm ourselves with the laws that are being applied at the present circumstance,” Howard told Australian radio.
“I think the Australian public is entitled to effective laws and God forbid that we should ever have a terrorist attack in this country,” he added.
Documents and material seized by Australian police during the investigation included photographs, computer hard drives, mobile telephones, PDAs and digital cameras, The Australian newspaper said.
Source: News Agencies