Muralitharan, who holds the world record of 800 Test wickets, said the Chennai-tweaker is on top at the moment.
"Ashwin, I think, is on the top at the moment as the best current Test spinner," Muralidaran was quoted as saying by Cricket Australia's (CA) website.
R Ashwin took maximum wickets -- 62 wickets in 9 Test matches -- in 2015. While in the year 2016, he is second highest wicket taker in T20Is in 2016 after Jasprit Bumrah.
Muralitharan also hailed Austrlian Nathan Lyon, who he feels bowls in different conditions.
"Lyon is a very good bowler, a very good off-spinner. He has proven himself in Test cricket and has taken a lot of wickets for Australia. He bowls in different conditions (in Australia) which are not much helpful for spin but on the turning wickets he has taken some wickets."
The 44-year-old Sri Lankan, who had worked with the Australians as a consultant bowling coach in 2014, said the Kangaroos start as favourites when they take on Sri Lanka in the three-match Test series later this month.
"Australia is favourite at the moment because they have played good cricket in the recent past. Sri Lanka on other hand is struggling a bit in all forms of the game so Australia will have an edge over Sri Lanka," he said.
"They have a chance of winning the series because the Sri Lankan side is very inexperienced as lot of players retired recently and they are rebuilding the side so they won't be strong enough."
"Therefore, Australia I think will have a good chance of winning the series. If they use the conditions properly and play their spinners well they definitely have a chance."