Hair, who controversially no-balled Muralitharan seven times for throwing in a Melbourne test in 1995, also said in Saturday's Herald Sun newspaper that the Sri Lankan had bowled illegally a number of times during his team's 11-run loss to Pakistan at the World Cup last week.
"A couple of current umpires have said to me, 'Something is wrong', but they prefer to let it go," said Hair, who umpired 78 tests between 1992 and 2008.
"There is still a lot of doubt about his deliveries.
"A few (officials) have told me, 'There is definitely something wrong with his action, but I'm not going to call him'.
"They are the ones who have to live with that.
"If you're an umpire you're meant to uphold the law so both teams get a fair shake.
"There's been some umpires who think, 'I'm on a good wicket here, I'm making good money, I won't rock the boat'.
"It's not my style, it's obviously theirs."
Doubts over his bowling have dogged Muralitharan since he was no-balled by Hair in 1995 but the 38-year-old Sri Lankan's bowling was cleared by the International Cricket Council (ICC) twice.
Extensive tests concluded that Muralitharan's action "created the optical illusion of throwing" and because of an elbow deformity, the bowler's arm remains bent in delivery and does not straighten.
Muralitharan is the leading wicket-taker in cricket in both the test and one-day forms of the game.
"I watched a few of his deliveries in his game against Pakistan and I noticed the last few overs when he was really getting some turn on the ball, those wouldn't have complied under scrutiny," Hair added.
"But this is his last World Cup, he's going to bow out with a lot of fanfare and no umpire will be bothered by it."
Hair's comments are certain to add spice to Australia's World Cup clash with Sri Lanka in Colombo on Saturday.
The controversial Australian, once described by former Pakistan captain Imran Khan as an "umpiring fundamentalist", was temporarily banned from officiating in 2006 after Pakistan became the first country to forfeit a match in more than a century of test cricket after a "walkout".
He had suggested they had tampered with the ball. Some leading cricket figures in the sub-continent suggested he was biased against their teams, a charge he denied.
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