Both Jayawardene and Herath had returned from Bangladesh having missed Twenty20 and one-day international matches there due to injuries. Thirimanne returned home from United Arab Emirates last December midway through playing Pakistan.
Uncapped seam bowler Chathuranga de Silva will take Herath's place if the senior hasn't recovered in time for the tournament starting March 16.
Sri Lanka would have four specialist spin bowlers if Herath returns, including allrounder Sachithra Senanayake. There are eight specialist batsmen, including seam bowling allrounders Angelo Mathews and Thisara Perera.
Squads:
WorldT20: Dinesh Chandimal (Captain), Lasith Malinga, Tillakaratne Dilshan, Kusal Perera, Kumar Sangakkara, Mahela Jayawardene, Lahiru Thirimanne, Angelo Mathews, Thisara Perera, Nuwan Kulasekara, Suranga Lakmal, Sachithra Senanayake, Ajantha Mendis, Seekuge Prasanna, Rangana Herath or Chathuranga De Silva.
Asia Cup: Angelo Mathews (Captain), Dinesh Chandimal, Tillakaratne Dilshan, Kusal Perera, Kumar Sangakkara, Mahela Jayawardene, Lahiru Thirimanne, Ashan Priyanjan, Thisara Perera, Lasith Malinga, Nuwan Kulasekara, Suranga Lakmal, Sachithra Senanayake, Ajantha Mendis, Chathuranga De Silva.