Mr Cairns, 45, denies charges of perjury and perverting the course of justice at Southwark Crown Court.
He is accused of falsely declaring under oath that he had never cheated at cricket in a 2012 libel case.
Justice Nigel Sweeney said on Friday he would accept a majority verdict.
Mr Cairns, who is one of New Zealand's greatest all-rounders and played 62 Tests from 1989 to 2004, is also accused of perverting the course of justice by inducing a fellow cricketer to give a false statement.
The jury of seven women and five men will resume their deliberations on Monday.
In the 2012 libel case - England's first Twitter libel trial - Mr Cairns won damages of $130,000 (£90,000) by successfully suing Indian Premier League chairman Lalit Modi over a 2010 tweet, which accused the cricketer of match-fixing while captain of the Chandigarh Lions in the now-defunct Indian Cricket League in 2008.
The prosecution at his current trial argued Mr Cairns had lied when he promised during the earlier trial that he had never cheated.
He is also accused of perverting the course of justice by inducing fellow New Zealand cricketer Lou Vincent to give a false witness statement in a Skype call.
Mr Vincent told the court that Mr Cairns had approached him to suggest he deliberately play badly for Chandigarh Lions and said he had helped to fix matches under "direct orders" from Mr Cairns, which the defendant denies.
The trial has also heard evidence from a host of cricketers including current New Zealand captain Brendon McCullum, former captain Daniel Vettori, former Australia captain Ricky Ponting, former New Zealand all-rounder Chris Harris and bowler Andre Adams.
During the case, Mr McCullum told the court Mr Cairns had approached him with a "business proposition" in a hotel room in Kolkata, India, in 2008, during the Indian Premier League, which involved match-fixing.
Mr Cairns's former adviser, Andrew Fitch-Holland, of Burton Road, Manchester, is also accused of perverting the course of justice. He denies the charge.
Jurors in the trial in London of ex-New Zealand cricket captain Chris Cairns have been sent home for the weekend after failing to reach a verdict on their second day of deliberations.