The former Australian captain's two-year term as India coach, arguably the most high-profile and nerve-wracking job in the business, ends after the showpiece event finishes on April 28.
India's cricket chiefs, who are known to move fast only when it comes to financial windfalls, have not even begun negotiations with Chappell, preferring to keep their options open till after the World Cup.
"What is the rush?," Board of Control for Cricket in India (BCCI) secretary Niranjan Shah told AFP. "Our first priority is to do well at the World Cup, other things can wait."
There is little concern for the fact that one tournament alone cannot judge a good or bad coach. Or that Chappell may understandably want an early settlement on his future.
The 58-year-old has so far declined to comment publicly if he wants to continue in a job that reportedly gives him an annual salary of US$300,000 plus handsome perks.
For the record, Chappell prefers to play with a straight bat.
"I can't say about the future. I know as much as you probably do. Right now, I'm thinking about the World Cup."
No other Test-playing nation has so far publicly indicated their interest in hiring Chappell, perhaps waiting for the BCCI to make up its mind.
The outspoken Chappell has made more headlines in 22 months as India coach than his predecessor, the genial John Wright of New Zealand, did in five years on the job.
His public spat with former captain Sourav Ganguly divided the cricket-crazy nation like never before, as did his policy to continue experimenting with the batting order at the cost of the team's success.
Chappell has been rebuked by the country's lawmakers for suggesting that "MPs are paid to talk in parliament" and was assaulted by a fan for ignoring players from the eastern state of Orissa.
Even his desire to take a quiet holiday with his wife, Judy, in the backwaters of Kerala ahead of the World Cup created a ruckus with the local police.
The owner of the houseboat where the couple was staying was hauled up by police for not reporting the presence of foreigners as required by law.
It is rumoured that the local media forced police to take action against the houseboat owner because journalists were peeved they were not informed the Indian cricket coach was holidaying in the area.
Under the Chappell-Dravid combine since July 2005, India have played 18 Tests and 59 one-day internationals with results indicating an upward swing in the team's fortunes.
Of the 18 Tests, India have won seven and lost four with seven drawn. Of the 59 one-dayers, the team has won 31, lost 25 with three games ending in no-results.
"No one can convince me that Chappell has not done a good job so far," said former captain and respected TV commentator Ravi Shastri, who was part of the BCCI panel that interviewed the Australian in 2005.
"But will the BCCI retain him? Your guess is as good as mine."
Chappell, one of the finest batsmen of the modern era, retired in 1984 with 7,110 runs from 87 Tests at an average of 53.86 and 24 centuries, including two in his first and last matches.
He also scored 2,331 runs in 74 one-dayers and even though elder brother Ian Chappell was regarded a better captain, Greg won 21 of his 48 Tests as Australian skipper and lost only 13.