The BCB were annoyed Whatmore put his hand up for the Indian job while his current charges were still involved in a World Cup campaign in the Caribbean.
"We are in the middle of a very high-profile tournament. At this stage any such interest of the coach would certainly distract our team," Riazuddin Al Mamun, a joint-secretary of the BCB, told.
"He should not have said so, when we have a contract with him."
The Sri-Lankan born Whatmore confirmed his interest in taking over the reins in India after Chappell handed in his resignation on Wednesday, two weeks after the 1983 champions' first-round exit from the World Cup.
"If the opportunity comes along, surely any person who is a professional coach and prides himself in doing a good job would be interested in coaching the Indian team," Whatmore had told an Indian news channel.
Whatmore coached Sri Lanka to World Cup success in 1996 and has worked wonders with the Bangladesh team, who effectively condemned India to an early flight home from the Caribbean after a surprise victory in the group phase of the competition.
Bangladesh reached the second round of the tournament for the first time this year but remain rooted to the bottom of the standings after suffering heavy defeats against Australia and New Zealand in their opening two Super Eights matches.
Whatmore's present contract with the BCB ends in May.
He took charge of the team in the aftermath of 2003 World Cup, where Bangladesh failed to win any of their six matches including those against Canada and Kenya.