Kaneria and fellow Essex bowler Mervyn Westfield were arrested last year on charges of spot-fixing during a Pro40 one-day match against Durham in 2009.
Kaneria was later released without being charged but Westfield faces criminal proceedings.
The 30-year-old leg spinner appeared before an integrity committee of Pakistan Cricket Board (PCB) on Monday but was not cleared of spot-fixing.
Sindh high court judges adjourned the case until September 27.
The PCB's legal adviser Taffazul Rizvi said the board wanted tapes of the police investigation from Kaneria.
"For the first time Kaneria's counsel has accepted that the tapes exist but they have not submitted these before the court so we have to contact our lawyer in England and try to bring those tapes," Rizvi told AFP.
The PCB will follow the court's verdict, Rizvi added.
Kaneria's lawyer Farogh Naseem said the police tapes are with leg-spinner's British lawyer Steve Haurigan.
Kaneria, a wily leg-spinner who has taken 261 wickets in 61 Tests – the most by any Pakistani spinner – expressed his disappointment at the delay.
"I am doing my best to clear my name but with the adjournment I have lost chance to play against Zimbabwe next month," Kaneria told AFP. "I have not lost heart and will do everything to revive my career."
Kaneria was dropped mid-way from the tour of England in August last year and sent home. Two months later he was selected for the series against South Africa but was withdrawn at the last minute.
Former Pakistan captain Shoaib Malik is also awaiting clearance from the committee after suspicions of match-fixing against him.
The PCB was forced by the International Cricket Council to form an integrity committee after a separate spot-fixing case in England last year ended in lengthy bans for Salman Butt, Mohammad Asif and Mohammad Aamer.
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