"We are trying to finalise the coach soon, but it will not be before the Indians finish their interviews this week," Jayantha Dharmadasa, chairman of the committee running Sri Lanka Cricket (SLC), told AFP on Monday.
"We have to realise that the Indian board is the richest in the world and coaching the Indian team is a prestigious job. Since the Indian board kept things on a hold, our candidates wanted some time as well."
Australians Greg Chappell and Tom Moody are short-listed by both countries to replace the outgoing coaches: John Wright from India and John Dyson from Sri Lanka.
Dharmadasa had earlier set a May 13 deadline for naming a new coach, five days before the Board of Control for Cricket in India (BCCI) interviews its candidates.
Chappell, Moody, Mohinder Amarnath of India and Desmond Haynes of the West Indies are due to appear before BCCI officials in New Delhi on Thursday.
Sri Lanka hope to fly Chappell, Moody and another Australian Dean Jones to Colombo after Wednesday to hold their own discussions.
Moody, 39, currently hired by English county Worcestershire as its cricket director, is regarded as the overwhelming favourite for the Sri Lankan job after being recommended by pace spearhead Chaminda Vaas.
But if the Indians choose the former Australian all-rounder, the SLC were expected to opt for either Chappell or Jones. Two former Sri Lankan players, Roy Dias and Rumesh Ratnayake, are also in the fray.
Dias, 53, was on the Sri Lankan coaching staff at the 1999 World Cup in England. Ratnayake, 41, was the national team's bowling coach till 2000.