The claims are said to be based on a leaked cache of secret files. It broke as the year's first Grand Slam got underway in Melbourne.
Novak Djokovic, the world number one, is the only one who admitted he was approached.
The incident took place on the eve of the first round of a match in Saint Petersburg in 2007, he says.
“I was approached through people who were working with me at that time,” he says.
“And of course we threw it right away. Somebody may call it an opportunity. For me that’s an act of unsportsmanship, a crime in sports, honestly."
Tennis officials were quick to respond.
"The Tennis Integrity Unit and the tennis authorities absolutely reject any suggestion that evidence of match-fixing has been suppressed for any reason or isn't being thoroughly investigated," said Chris Kermode, president of the Association of Tennis Professionals.
The leaked files include details of an investigation into a 2007 match between Nikolay Davydenko and Martin Vassallo Arguello, which found insufficient evidence of corrupt practice.
The report said the probe uncovered syndicates in Russia and Italy making hundreds of thousands of dollars betting on matches investigators thought to be fixed.
The key group of 16 suspect players had not been targeted in any crackdown, it said, questioning the effectiveness of the Tennis Integrity Unit.
Kermode said the TIU had won 18 convictions including six life bans since it was set up in 2008, adding it "has to find evidence as opposed to information, suspicion, or hearsay".