BCCI president Ranbir Singh Mahendra, however, announced that efforts were on to get in touch with 2-3 other former internationals, all from abroad, before the final selectionwas made.
"You will get to know the name of the new coach by June 15," he said while briefing newspersons on the deliberations at the two-hour meeting of the six-member committee formed to finalise a name for the top job.
Along with Amarnath and Patil, former Australian Test players Greg Chappell and Tom Moody have also been shortlisted in the maiden meeting of the committee, chaired by Mahendra at a five star hotel here.
But Mahendra refused to divulge the names of the other internationals BCCI was planning to sound out before making its final choice.
The candidates would be called for an interview, the date of which would be finalised after considering their availability, he said.
The high-profile commmittee also comprised former Indian captains Sunil Gavaskar, S Venkatraghavan, Ravi Shastri and ex-president of BCCI Jagmohan Dalmiya, with board secretary S K Nair as the convenor.