Cricket officials in Colombo said the off-spinner had not officially told the authorities about changing his mind after Australian Prime Minister John Howard called him a "chucker".
Local daily Sunday Leader argued that Sri Lanka Cricket (SLC) should encourage Muralitharan to join the rest of the team and travel to Australia or else the Sri Lankan team would be like a "one armed boxer".
However, the Sunday Island newspaper encouraged Muralitharan to stay away from Australia, where he had been called for "throwing".
Shortly after returning home last month from Zimbabwe, where he set the world record for the highest number of Test wickets, Muralitharan said pressure from Australia and England fuelled the ban on his controversial "doosra" delivery.
"Even if they insist, I don't mind, I can bowl several others," Muralitharan said of his controversial delivery.
"This ban is because of pressure from Australia and England. There is no problem in Asia. No one in Asia has complained about it."
Sri Lanka last week set aside its bid to sue the International Cricket Council (ICC) and instead plan to plead against its decision to outlaw Muralitharan's "doosra".
The Government, after talks with lawyers, decided to change tactics and go before the world governing body of the sport to appeal Muralitharan's case, Prime Minister Mahinda Rajapakse's spokesman Rohan Weliwita said.
Muralitharan, whose unorthodox action has seen him being no-balled for "throwing" in the past, came under fresh scrutiny because of the "doosra" and was told last month that if he persists with it he could face a year-long ban.