The board is looking for a successor to Greg Chappell, who quit following India's shock first round exit from the World Cup.
"He can be regarded as one of the candidates," said the official, who did not want to be identified.
"Whatmore looks like he is interested."
Whatmore guided Sri Lanka to the World Cup in 1996 and helped unfancied Bangladesh reach the second round for the first time this year in the Caribbean after a shock win over India.
The 53-year-old decided not to renew his contract with Bangladesh, which ran out at the end of April, but agreed to coach the team in a series against India this month.
Senior Indian board officials are likely to meet the outgoing Bangladesh coach during a two-Test series, which starts on Friday.
Indian media reported on Thursday that former skipper Ravi Shastri, the current cricket manager who is on the committee to pick the new coach, has held discussions with Whatmore.
The Indian board wants to appoint the new coach before the team leaves for tours of England and Ireland next month.
