Ex-Sri Lanka captain Marvan Atapattu, former opening batsman Romesh Kaluwitharana and another national player Ruwan Kalpage are among the local applicants.
SLC advertised for it after incumbent Graham Ford announced that he would leave the job in January next year.
Peter Moores, a former England coach and Paul Farbrace, who was assistant coach with Sri Lanka until 2009, are among the overseas aspirants alongside Prasad.
SLC said the deadline for applications has been extended until October 31.