Sources in Sri Lanka Cricket (SLC) said five foreign coaches had filed applications by the October 6, the closing date for applications.
The SLC interim committee is to decide on a possible appointee at the SLC executive committee meeting to be held on October 20.
The position fell vacant after Marvan Atapattu resigned in September following the successive home series defeats against Pakistan and India.
Atapattu took over from Paul Farbrace who left to join the England coaching staff in 2013.