Australia heads into quarterfinals against a formidable Indian side on Thursday even as Ponting grapples with an indifferent form and it could be the final week for the 36-year-old as captain.
The Sydney Morning Herald reported a Cricket Australia official saying that there should be a discussion by the board on whether Ponting should lead the team against Bangladesh even though his position as a player was not in jeopardy.
"We need to be looking at the future," the senior official was quoted as saying by the paper.
"It's time for us to make a change."
Ponting has been under scanner since the Ashes series where he earned the dubious distinction of being the only Australian skipper to lose the urn three times.
In the World Cup, the right-handed batsman have been in news for wrong reasons after being reprimanded by ICC for damaging a TV screen with his protector during Australia's first match against Zimbabwe.
He again hit the headlines after publicly warning teammate Steve Smith and also faced criticism for standing his ground until he was given out on a TV umpire's review despite knowing he'd got a thick edge during their defeat to Pakistan.
"We're waiting for the next thing to blow up," the official said.
"We don't go a game without there being some issues with him," he added.
Selectors will huddle up to name the Australian squad for the Bangladesh series after Australia's World Cup campaign is over. Australia will play a three-match ODI series against Bangladesh starting from April 9.