Muralitharan's manager Kushil Gunasekera said the record-breaking bowler was miffed over what he felt were "degrading" articles written by Bedi in newspapers and magazines about the off-spinner's controversial bowling action.
Bedi, a former Indian Test captain and classical left-arm spinner, said he stood by his opinion that Muralitharan's bowling did not conform to the laws of the game and the Sri Lankan was welcome to sue.
"The International Cricket Council (ICC) is squarely to blame for allowing Muralitharan to get away with it," said Bedi, a member of the famed Indian quartet of the 1970s who retired with 266 Test wickets.
"They have to realise that I have nothing personal against Muralitharan. I have never met him, never said hello, never shaken hands with him.
"But in my book, I've never seen him bowl either."
Muralitharan, according to his manager, had instructed lawyers to initiate legal proceedings against Bedi, an outspoken critic of the Sri Lankan who is Test cricket's most successful bowler with 529 wickets.
"Bishen has always written very degrading articles calling Murali a cheat and all that stuff," manager Gunasekera said. "We have taken serious note of those articles and will send them to Bedi's lawyers."
"I have no lawyers," responded Bedi. "Let them send a letter, they will have to send a million letters to various people.
"I am talking about the spirit of the game being violated and like I said the ICC is to blame.
"It's not a question of him being a cheat, he's been given permission to bowl like that. He's not the only one around who chucks. The problem is not with the bowlers - it lies in the ICC's inefficiency to control them.
"Bob Woolmer (ICC's cricket development manager) had said recently that Murali had a shot put action and Pakistani fast bowler Shoaib Akhtar had the action of a javelin thrower.
"What do shot putters and javelin throwers do anyway?," Bedi asked.
Muralitharan, 32, has had to defend his bowling action since being called for throwing on the 1995-96 tour of Australia.
He was again reported by English match-referee Chris Broad during a home Test series against Australia in March, forcing the sport's governing body to ban his 'doosra', a delivery that spins away from right-hand batsmen.
The Sri Lankan is still undecided whether he will tour Australia later this month for a two-Test series after Australian Prime Minister John Howard called him a "chucker."