After the BBC and BuzzFeed reported top players, including Grand Slam title-winners, were suspected of match-fixing but never punished, Murray said the fight against corruption must be transparent.
"If there is corruption in any sport, you know, you want to hear about it," said the world number two, after beating Alexander Zverev in the Australian Open first round.
"As a player you just want to be made aware of everything that's going on. I think we deserve to know everything that's sort of out there," he added.
Tennis officials reacted angrily to the report, refuting any suggestion of a cover-up and criticising its release just before the start of the season's first Grand Slam.
But Murray said players should not have to read about the match-fixing claims in the media, and that tennis authorities should be more open about the situation with their participants.
"I just think that it should be tennis that does a better job of explaining -- they (players) shouldn't have to read it in the press," Murray told reporters.
"I think the more proactive you are with educating young players, the better on matters like this."
Murray said, unlike world number one Novak Djokovic who was targeted earlier in his career, he had never been approached to fix a match.
Murray also took aim at organisers for allowing a betting company to sponsor this year's Australian Open, a move which has already provoked criticism.
"I don't really understand how it all works. I think it's a bit strange."
Other players have also detailed approaches and according to Australian media, police are closely watching the first round of the Australian Open for suspicious results.
The controversy is just the latest to hit the sports world, after allegations of doping cover-ups rocked athletics and football body FIFA was engulfed by a string of corruption scandals.
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