The heavily-scrutinised Sri Lankan spinner has dared Australian fans to heckle him as he chases the nine wickets he needs to pass Warne's world record tally of 708 in the Australian great's own backyard.
Sri Lanka take on the world champion Australians in Tests in Brisbane and Hobart in November and a one-day tri-series with India and Australia early next year.
"He is comfortable with what Australia is like," Muralitharan's manager Kushil Gunasekera told Melbourne's Herald-Sun newspaper Thursday.
"He understands the harassment given by spectators will only make him more inspired and motivated. It will help him bowl better.
"Murali is happy to be taking on that challenge because Australia is a real test. He will come to Australia."
But while Muralitharan is within touching distance of Warne's record, he has a poor record playing on Australian wickets.
In three Tests in Australia, Muralitharan has taken eight wickets at 63.12.
Muralitharan has endured a turbulent relationship with Australian crowds since he was no-balled for throwing by Australian umpire Darrell Hair in the 1995 Boxing Day Test in Melbourne.
After the 2005-06 tri-series, Muralitharan claimed Australian crowds were the world's worst and a disgrace to cricket.
He had vowed in 2003 he would never return to Australia after the abuse he received during the one-day series.
Even Australian Prime Minister John Howard labelled him a chucker.
Sri Lanka play Australia in Brisbane from November 8-12.