The Board of Control for Cricket in India (BCCI) has called former captains in for a brainstorming session on April 6 and 7, where they will also hear Chappell's views on the team's miserable performance in the tournament.
Inderjit Bindra, a former BCCI president and still one of its most influential members, denied rumours in the media that the board had already decided to sack both Chappell and Dravid.
"We are all disappointed but I can promise you there will be no knee-jerk reaction," Bindra told reporters.
"We will hear both Chappell and Dravid and see how best we can find a long-term solution.
"By making sweeping changes we are not going to improve Indian cricket overnight."
Chappell, former Australian Test captain, has been coach of India for a two-year term that was due to end after the World Cup, with the Indian press predicting he would either be sacked from the job or quit on his own after returning from Trinidad this week.
"The meeting next week has been called to essentially extend our support to the team in this hour of despair," Bindra said.
"We are appalled at the manner in which the media, especially TV channels, has reacted to the team's early exit, and the BCCI cannot just sit back and allow the players to be torn apart in public.
"The team never claimed it would come back with the World Cup," the BCCI member added.
"To suit their commercial interests, some of these TV channels first created unprecedented hype and now have been behaving in a regrettable manner."
Bindra was referring to broad coverage of publicity-seeking stunts like street demonstrations, effigy burning and mock funerals of cricketers that took place across India last week.
The BCCI needs to settle the captaincy and coach issues soon, as the team travels to Bangladesh in May for a three-week tour comprising two Tests and three one-day internationals, before embarking on a gruelling schedule till March next year that includes a minimum of 15 Tests and 42 one-day internationals around the world.
It remains to be seen if senior players such as Dravid, Sachin Tendulkar, and Sourav Ganguly will continue playing limited-overs cricket, while veteran spinner Anil Kumble, India's most successful bowler in both forms of the game, said he would quit one-dayers after the World Cup to concentrate on Test matches.