Atapattu is currently the batting coach of the national team.
Alongside Atapattu, Mark Davies, coach of English county side Sussex, is the other contender.
There were five candidates who were to face a seven-member panel but Steve Rixon, the current Australian fielding coach, did not turn up.
Sri Lanka Cricket is trying to find a successor for Graham Ford who will leave the job to take charge of Surrey in the English County Championship.
Sri Lankans Romesh Kaluwitharana and Ruwan Kalpage and Indians Venkatesh Prasad, Lalchand Rajput and Mohit Soni were the other shortlisted candidates.