Muralitharan, who has refused to tour Australia in the past because of crowds taunting his unusual bowling action, wants to show why he is one of the best bowlers in the world, skipper Mahela Jayawardene said.
"He hasn't played here for 10 years in a Test match and he's pretty geared up I think. He feels Australia is one of the places that he has to challenge himself," Jayawardene said.
"This is probably a place where he has to prove he's one of the top bowlers in the world, so I think he's looking forward to the challenge."
'Murali' needs just nine wickets to overhaul Warne's 708 Test scalps in the Test matches in Brisbane and Hobart starting on November 8 and 16.
The Sri Lanka tour follows Australia's return home after a bitter series against India marred by the racial taunting of the team's only black player, Andrew Symonds, who was subjected to monkey noises and gestures.
There are fears that Muralitharan could receive unsportsmanlike treatment in Australia, where he has been called for 'throwing' on two previous tours and subjected to constant crowd calls of "no ball."
Sri Lanka coach Trevor Bayliss said there were "always idiots in every crowd" and it was near impossible to control the behaviour of fans.
"I don't know whether you're going to stop that 100 percent," he said.
"But I think the majority of people realise it's the wrong thing to do and don't get involved, there's just one or two idiots in every crowd."
Jayawardene said his team would challenge Australia but not get so carried away as to be involved in the antics seen in India.
"We have to be very aggressive with Australia, but to a certain extent sometimes if you go overboard you lose your own concentration as well, and we certainly don't want that to happen," he told a press conference.
"We will be aggressive, but not to the extent that we would get involved with silly incidents."
Australia captain Ricky Ponting said a little heckling from the crowd was to be expected.
"But when it gets a bit out of control like it did in the series just gone in India it becomes pretty disappointing and I think pretty embarrassing for the home team," he said.
Muralitharan's ultra-flexible bowling action has come under its heaviest scrutiny in Australia, where he has been called for throwing on two tours and has not played a full Test match since late 1995.
He boycotted Sri Lanka's 2004 visit after Australian Prime Minister John Howard labelled him a "chucker."
However, he returned for a one-off Test for the Rest of the World in 2005 and a one-day series in 2006, when he was unofficially reprimanded for making a one-fingered gesture to taunting spectators in Perth.
Sri Lanka will play a warm-up match in Adelaide starting Saturday.