The former world record holder was left out of Sri Lanka's 20-man preliminary squad for the December-January tour of New Zealand that features five One-day Internationals followed by two Test matches.
But officials were hopeful the prolific off-spinner, who has been out of the game since August due to surgery on his bowling shoulder, may be available for the two Tests at Hamilton (January 15-19) and Wellington (Jan 22-26).
"Muralitharan was not included in the list of probables because he has not been medically cleared to play," said Sri Lanka Cricket spokesman Ray Illangakoon on Wednesday.
"We are monitoring his improvement and will decide later if he can play the Test matches."
Muralitharan will be told next week by his Melbourne-based surgeon, David Young, when he can start playing, Illangakoon added.
The 32-year-old was Test cricket's most successful bowler with 532 wickets till Australian Shane Warne overtook him on the recent tour of India and took his tally to 541.
Muralitharan, whose career was been marred by accusations of chucking, has been banned by the International Cricket Council from bowling the going-away delivery -- the 'doosra' -- because of his controversial action.
Sri Lanka will travel to New Zealand without veteran wicketkeeper Romesh Kaluwitharana who announced his retirement on Tuesday after being left out of the preliminary squad.
Kaluwitharana, 35, was best known for his aggressive batting and was part of Sri Lanka's World Cup-winning team in 1996.
His decision to quit was sparked by a wrist injury sustained on the recent tour of Pakistan. Sri Lanka drew the series 1-1.
Sri Lanka's preliminary squad:
Marvan Atapattu (capt), Mahela Jayawardene, Sanath Jayasuriya, Kumar Sangakkara, Tillakaratne Dilshan, Chaminda Vaas, Upul Chandana, Nuwan Zoysa, Dilhara Fernando, Rangana Herath, Saman Jayantha, Thilan Samaraweera, Thilina Kandamby, Kaushal Lokuarachchi, Lasitha Malinga, Ian Daniel, Farveez Maharoof, Nuwan Kulasekara, Jehan Mubarak, Prasanna Jayawardene.