Modi was seeking to recoup £1.5 million pounds (US$2.13 million) in costs from a libel suit he lost when former New Zealand star Cairns successfully argued he had been defamed by the Indian cricket entrepreneur.
However, the Weekend Herald, said Modi had now "given up trying to claw back costs".
Cairns cleared of match-fixing perjury charges
Cairns, who no longer lives in New Zealand, declined to comment "but his UK solicitor Rhory Robertson confirmed a Notice of Discontinuance had been filed by Modi to halt proceedings", the newspaper said.
The five-year legal battle began in January 2010 when Modi alleged in a tweet that Cairns had been involved in match-fixing.
Cairns won the libel case in 2012 and in an eight-week trial last year he was also found not guilty of perjuring himself in the defamation hearing.
Match-fixing case: No winners in Cairns trial: NZ Cricket
Modi launched his lawsuit based on evidence in the perjury case when New Zealand captain Brendon McCullum and former Test batsman Lou Vincent claimed they had been approached by Cairns to fix matches.
Cairns, 45, said after the perjury trial that years of litigation had left him "penniless".
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