The Aussie leg spinner hoped the Sri Lankan had not been influenced by his controversial former captain Arjuna Ranatunga.
"I'm sure the Australian public would love to see him here," the Australia captain said.
India's top envoy Nirupam Sen said the ace spinner is "pride and pleasure" for Indians as well.
Muttiah Muralitharan will need to prove his fitness before joining the Sri Lankan team for the ODI series in New Zealand.
The Zimbabwe batsman was suspended for one Test for his comments regarding Sri Lanka off-spinner Muttiah Muralitharan.
The off-spinner has been advised by his Board and the ICC to not bowl his 'doosra.'
The Sri Lankan off-spinner equalled Courtney Walsh's world mark of 519 Test wickets on the first day of the first Test against Zimbabwe.
"Murali has so much cricket left in him that I have little doubt that he will reach the 700-wicket mark in Test cricket," the former Sri Lankan batsman said.
The former Australian captain said the Sri Lanka off-spinner's action is legal.
The Sri Lankan off spinner will make a comeback to Test cricket in the series against New Zealand in January next year.
Indian captain Saurav Ganguly failed to make the cut for the ICC World XI preliminary squads, for October's Johnie Walker Super Series against Australia.
A look at Muttiah Muralitharan's wicket ways after the Sri Lankan off-spinner claimed a world record 709 Test wickets.
Sri Lanka Board officials said match referee Chris Broad made the report after the close of the third and final Test
Two former Australian test umpires have criticised cricket bible Wisden for selecting Sri Lankan Muttiah Muralitharan as the most valuable test bowler in history.
After being skittled out 120 in 42.2 overs, Australia had Sri Lanka reeling at 92 for 7 on the opening day of the first Test.
Muralitharan sat out nets on Sunday afternoon due to stomach upset and then suffered from stomach cramps throughout the night.
Muralitharan will resume bowling on March 17 after shoulder surgery while Zoysa is recovering from a knee injury.
The two spinners were summmoned as replacements for injured ace Muralitharan.
Sri Lanka's Muttiah Muralitharan had shoulder surgery overnight and will be back to full fitness in five months.
The Sri Lanka spinner will have surgery on a career-threatening shoulder injury on Monday.
The Sri Lankan off spinner was forced out of the second and final Test against South Africa after complaining of intense pain.
Rajneesh Gupta presents the interesting numbers from Day 1 of the second Test between Sri Lanka and India in Colombo.
The Sri Lanka off-spinner claimed his 528th wicket on the third day of the first Test against South Africa before the visitors closed play at 347 for 7.
The ace spinner will sit out of Sri Lanka's last Super League match against India in the Asia Cup following the death of his grandfather.
Warne has 520 career wickets, seven short of Sri Lanka off spinner Muttiah Muralitharan's world mark.
Sri Lanka captain Marvan Atapattu said they would struggle against the world champions without the off spinner.
A matchmaking website features a purported profile of the Sri Lankan off-spinner.
The off-spinner has been named in a 16-man squad to tour Australia this month.
James Anderson joined an elite band of bowlers with 500 test wickets and Ben Stokes plundered a vital half century as England took command of a low-scoring third Test against West Indies at Lord's on Friday.
The Sri Lanka spinner said it was a key factor in him equalling the world record for Test wickets.
Former Australia Test umpire Lou Rowan said players are unwilling to comment on the bowler's action because they will be accused of racism.
Sri Lanka defeated Pakistan by 201 runs on the final day of the first Test on Sunday.
The ace off-spinner, who underwent a hernia operation in November, is likely to play in Thursday's game.
The ICC chief said match officials are well within their rights to raise concerns about any delivery from any bowler.
Australia reached 80 for three in their second innings, a 74-run lead after Sri Lanka were bowled out for 407 in their first innings on the third day.
Muttiah Muralitharan became the third bowler in history to claim 500 wickets as Sri Lanka bundled out Australia for 120 on the opening day of the second Test.
Graeme Smith also moved up seven places to 12th in the batting ratings.
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