Haneef, an Indian national who emigrated to Australia from Britain last year, is a distant cousin of Kafeel and Sabeel Ahmed, two suspects held in Britain in connection with two bomb-laden cars found in London on June 29 and an attack on Glasgow airport the next day.
Kafeel Ahmed is being held under police guard in UK hospital where he remains in a critical condition from severe burns caused by the Glasgow attack.
The documents cited by the Australian said police do not want to release Haneef because they suspect he "provided support to the terrorist organization responsible for the terrorist acts in London and/or Glasgow."
Investigators have seized several computer hard drives, PDAs, flash drives and computer disks as well as phones and digital cameras belonging to Haneef and his associates, the paper reported.
It quoted officials as saying the inquiry had been complicated by the need to process the large volume of electronic data they had found and check it with material held by British authorities.
The Australian said police were likely to urge Brisbane magistrates to allow them to hold Haneef for another 72 hours, adding that investigations could take up to two more weeks to complete.
"If Mr Haneef was released from detention, it would be more difficult for authorities to effectively monitor his movements and who he communicates with, either in Australia or overseas," the paper quoted government documents saying.