Muralitharan took 2-25 against New Zealand on Friday
Muttiah Muralitharan is to remain with Sri's Lanka World Twenty20 squad after making "significant progress" in recuperating from a groin injury.
Sri Lanka Cricket said the spinner was out of the tournament on Monday due to an injury picked up in the preliminary round match defeat to New Zealand.
However, team physio Tommy Simsek now says the 38-year-old has stepped up his training and can resume bowling soon.
Captain Kumar Sangakkara revealed: "We have not ruled him out completely."
The 32-year-old wicketkeeper-batsman added: "We are going to give him a few more days to try and see whether he can get on the park and compete at 100% for us."
Sri Lanka progressed to the second round of the tournament, courtesy of a 14-run victory over Zimbabwe via Duckworth Lewis, and will take on the West Indies on Friday.
Relatively inexperienced off-spinner Suraj Randiv, 25, with nine one-day internationals behind him, made his Twenty20 debut in that match in place of Muralitharan, who it was revealed had strained his right adductor (thigh) muscle during the two-wicket loss to New Zealand on Friday.
He took 2-25 in the exciting tournament opener, and put Sri Lanka's opponents on the back foot until a late burst of scoring by Jacob Oram and Nathan McCullum gave New Zealand an unlikely victory.
Muralitharan has more international wickets than any cricketer, with 792 in 132 Tests and 512 in 334 limited-overs internationals.
He has 13 wickets in 10 T20 internationals with an impressive average of 18.46 and an economy rate of 6.15.
Left-arm fast bowler Thilan Thushara has been called up as additional cover for Muralitharan.
Ashley de Silva, the SLC's head of cricket operations, said: He will only be considered for selection if Muralitharan is unable to take further part in the World Twenty20."