Ponting, who let slip Australia's 12-year grasp on the World Cup last week - just three months after their heavy Ashes defeat - has already hinted that he may step down.
Cricket Australia said a squad for next month's three-match one-day tour of Bangladesh was expected to be announced on Wednesday, effectively setting a deadline for the veteran skipper.
Ponting, 36, returned home on Sunday following Australia's quarterfinal exit from the World Cup at the hands of India, saying he was considering his position this week.
"I'll have the opportunity over the next couple of days to reflect on where things are headed for me and certainly what direction I feel things are heading for the betterment of Australian cricket," the Test and one-day captain told reporters.
"I have to really decide what I think is right for me and the team going forward."
Australia play three one-day matches against Bangladesh on April 9, 11 and 13, with Ponting previously stating that he wanted to lead the team on the tour.
But Ponting has since suggested he could quit as captain, saying he was prepared to play on under the likely leadership of his deputy Michael Clarke and bat anywhere in the order.
"I see myself as a leader around the group, simple as that, whether I'm captain or not I still think I've got a lot to offer as far as leadership qualities go," he said.
Though heartened by support of team-mates and senior officials, Ponting said he was "absolutely" prepared to drop down the order and step down as captain "if that's what they (CA) and I believe is the best way forward".
Ponting, who has been under attack since the 3-1 Ashes series defeat to England, scored a fighting 104 but it was not enough to prevent India from knocking the champions out in last Thursday's quarterfinal in Ahmedabad.
He has now presided over the end of Australia's 12-year run as World Cup champions after his third Ashes series defeat as captain to England.
Ponting, who has been captain for nine years, had a difficult World Cup, taking a reprimand from the International Cricket Council after smashing a dressing-room TV in a fit of fury after being run out against Zimbabwe.
He was also criticised for angrily throwing the ball to the ground after colliding with team-mate Steven Smith during their victory against Canada, and for failing to walk in the group match defeat by Pakistan.
Australia sets Ponting captaincy deadline
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