The Board of Control for Cricket in India (BCCI) has called former captains for a brainstorming session on April 6 and 7 that will also hear Chappell's views on the team's dismal performance in the Caribbean.
India, the 1983 champions and 2003 finalists, failed to advance to the Super Eights round after losing two of their three matches in group B of the preliminary stage.
India were stunned by Bangladesh in their first match, then hammered first-timers Bermuda in the second before losing a must-win game against Sri Lanka to bow out of the tournament.
It was India's worst World Cup performance since the second edition in 1979 in England, where they had also won just one match.
Inderjit Bindra, a former BCCI president and still one of its most influential members, rubbished media speculation 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, a former Australian captain, has served as India's coach for a two-year term that was due to end after the World Cup.
The Indian media predicted that Chappell would either be sacked from the job or quit on his own after returning from the Caribbean 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. 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 extensive coverage of publicity-seeking stunts like street demonstrations, effigy burning and mock funerals of cricketers that took place around the country last week.
India must quickly settle the captaincy and coach issues since the team travels to Bangladesh in May for a three-week tour comprising two Tests and three one-day internationals.
The BCCI has finalised a gruelling schedule for the team 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 like Sachin Tendulkar, Dravid and Sourav Ganguly will continue playing limited-overs cricket.
Veteran spinner Anil Kumble, India's most successful bowler in both forms of the game, had said before the World Cup that he would quit one-dayers after the tournament to concentrate on Test matches.