The 44-year-old former offspinner, still the highest wicket-taker in test cricket with 800 scalps, had a similar short-term consulting stint with Australia in 2014.
"Murali's got a lot of experience in Sri Lanka," Australia captain Steve Smith said. "He took a truckload of wickets.
"It's great to have someone like that helping our spinners in this series - to give us that insight. He's been really good around the group so far, and he's enjoying his time with us."
Muralitharan, who has been seen working with Australian spinners Nathan Lyon and Steve O'Keefe in the nets, said he was looking for such short-term jobs and had no problems helping the visitors plot against his own country.
"I'm not involved in Sri Lankan cricket at all because there are (other) people who are involved," Muralitharan, a perennial thorn in Australia's flesh during his playing days, told Cricket Australia website.
"Then, on and off, Australia offered me twice so I said 'why not' because you are passing on the knowledge to other people. It doesn't matter whether it's your country or other people.
Read more on SuperSport.
"Then, on and off, Australia offered me twice so I said 'why not' because you are passing on the knowledge to other people. It doesn't matter whether it's your country or other people.
Read more on SuperSport.
