"We will see what he wants and decide accordingly," BCB president M. Abdul Aziz told reporters on Thursday.
The board are also set to decide on the fate of captain Habibul Bashar, who has been criticised for a string of recent poor performances.
Bangladesh beat India in the group stages of the World Cup in the Caribbean to advance to the Super Eights, but have only managed a victory over South Africa in their six subsequent matches to miss out on a semi-final berth.
The BCB has formed a six-member committee to mull over the coach and captain situation immediately after Bangladesh return from the West Indies on April 26.
Sri Lankan-born Whatmore's two-year contract expires four days later and after he expressed an interest in the India post following Greg Chappell's resignation, the 53-year-old is not expected to renew his agreement with Bangladesh.
Should Whatmore leave, Bangladesh face a race against time to install an experienced coach for the home Test and one-day international series against India in May.
However, BCB sources have indicated that the board may ask Whatmore to stay on as coach until the end of the India series.
Since taking over after the 2003 World Cup, Whatmore has led Bangladesh to 33 wins in 86 one-day internationals and coached the side to a first ever Test victory, against three draws and 21 defeats.
On the field, Bashar has made just 93 runs in his seven World Cup innings to date at an average of 13.28, raising questions over his 'indispensable' tag in the one-day squad.
"We will name the coach and captain for the India series on April 30," BCB general secretary Mahbub Anam added.
"The captain and vice-captain will both be experienced members of the present squad."