The former Australia captain's two-year term comes up for renewal in May and with India all but crashing out of the World Cup on Friday, his chances of extending that contract appears to be very slim.
"Our agreement with the coach is until the World Cup, so that agreement is over. The board will decide on the future course of action," Indian board president Sharad Pawar told reporters.
A senior board official who did not want to be named told, "Greg was to discuss his future with Sharad Pawar during the Super Eights. But following the exit ... there is a lot of time to think about the future."
India, beaten by Sri Lanka on Friday, lost two of their three group matches in Trinidad and their slender hopes of progressing to the next stage hinge on the unlikely defeat of Bangladesh by debutants Bermuda.
With India's next international assignment in May (tour of Bangladesh), the board have ample time to decide on a coach.
Runners-up to Australia in the 2003 edition, India were touted favourites back home and expected to progress at least till the semi-finals.
Defeats by Bangladesh and Sri Lanka has resulted in pressure mounting on the board to make large-scale changes to the struggling team, dubbed as "Dad's Army" by the media for containing a number of ageing players.
Chappell's tenure with India has yielded mixed results since taking over in May 2005 from New Zealand's John Wright, who served as India's first foreign coach for almost five years.
A 1-0 Test series victory last year in the Caribbean after 35 years was one of the high points.
But the failure to qualify for the semi-finals of the Champions Trophy as hosts last year and the predicament of a first-round exit from the World Cup has not gone down well with cricket-crazy India.
"You cannot live down this World Cup exit in a long time," the official said.
"It is also on his (Pawar) mind that after taking over as the board president, the team has not performed in major tournaments.
"He (Pawar) is sure to feel the ignominy of this (team's) exit, coming right after the Champions Trophy.
"At the moment, he (Pawar) will be disappointed and will not be in a mood for discussions."