Leading candidates? Tom Moody and Dav Whatmore
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A committee has been put in place to find a replacement for India coach Greg Chappell, who resigned after their dismal performance in the World Cup.
The Board of Control for Cricket in India has said it will again consider the merits of any overseas candidate and will also appoint a team manager.
BCCI secretary Niranjan Shah said: "All options are open. The appointments will be announced after the World Cup."
The seven-man committee features three former Indian Test players.
The most high-profile of them is Sunil Gavaskar, while Ravi Shashtri - who will be the interim coach for the tour of Bangladesh - and retired umpire Srinivas Venkataraghavan are also on the panel.
Shastri has said he does not wish to do the job long-term.
Many former Test players and cricket pundits have argued that it is time for a homegrown coach after spells under Chappell and his predecessor, New Zealander John Wright.
One man who has expressed an interest in coaching India is Dav Whatmore.
He masterminded Sri Lanka's 1996 World Cup success and has since overseen some telling improvement from Bangladesh, leading them to victories over India and South Africa in this year's tournament.
Whatmore is in the process of leaving his job, while Sri Lanka coach Tom Moody is refusing to discuss his future.
Moody's Sri Lanka play a World Cup semi-final against New Zealand on Tuesday.