The former world record holder was left out of the 20-member squad for the December-January tour that features five One-day Internationals and two Test matches, but he could be taken back, spokesman Ray Illangakoon said on Sunday.
"Doctors have given him the green light to start bowling," said Illangakoon. "Now he has to start practices and depending on further tests, he could well be included in the squad."
The star off-spinner has been out of the game since August due to surgery on his bowling shoulder.
Muralitharan was told by his Melbourne-based surgeon, David Young, that he could go back to international cricket, Illangakoon said.
The 32-year-old was Test cricket's most successful bowler with 532 wickets until Australian Shane Warne overtook him on the recent tour of India and has since pushed his tally to 550.
Muralitharan, whose career was been marred by accusations of chucking, has been banned by the International Cricket Council (ICC) from bowling the going-away delivery -- the 'doosra' -- because of his controversial action.
However, new bowling rules drawn up by the International Cricket Council which have yet to be formally accepted by the governing body could end the controversy over the doosra.
Cricket officials said they have advised Muralitharan to refrain from bowling the doosra until the new bowling rules go into effect.
An ICC committee made up of former Test players, chaired by former India captain Sunil Gavaskar, has recommended a new rule allowing bowlers to straighten their arms by up to 15 degrees.
The earlier rule varies the amount of straightening allowed depending on the type of bowling. Spinners were restricted to five degrees, medium pacers to seven and a half degrees and fast bowlers to 10 degrees.
Under the proposed ruling, which will be put to the ICC chief executives' committee of the 10 Test-playing countries at its next meeting, in Melbourne, Australia, in February, almost all modern bowling actions would be legal.
Tests showed that the Sri Lanka star's elbow straightened by 14 degrees, nine degrees more than the current limit for spinners, when bowling the doosra.
Extensive research into the biomechanics of bowling over the past four years has revealed that almost every bowler straightens his arm before letting go of the ball.