The family had been on a summer holiday in West Mersea. They are believed to have got into difficulty after an incoming high tide caused the sand beneath their feet to give way.
No final decision has been taken and the group is still evaluating the proposal because airlines are considered a difficult business with limited profitability, the first source said.
The CJP, which launched protests last month over exam paper leaks affecting about two million students and linked to several suicides, rejected the announcement.
The scrutiny comes as the DGCA oversees one of the world's fastest-growing aviation markets while dealing with staff shortages after a year that included the Air India Dreamliner crash.
