At the moment, they are third in Group B, with matches against second-placed Mali and bottom side Ethiopia to come.
Malawi are scheduled to host Mali on 15 November and travel to Ethiopia for their final match four days later.
But FAM says Flames camping, which was slated for this Sunday, has been postponed until funding has been identified.
The statement says government, Flames main sponsor, did not provide financial resources for the previous fixture and remaining fixtures of the tournament.
“Government decision has left FAM no option but suspend camp training of the Malawi national football team to avoid incurring debts that FAM would not be able to settle,” the statement, signed by FAM general secretary Suzgo Nyirenda, says.
“FAM would like to further note that in the event that funding is not identified, it will be compelled to withdraw the Flames from the on-going Africa Cup of Nations.”
The cut-off point for a decision will be on November 5, according to Nyirenda.
The effect of such withdrawal is that apart from being fined hefty fee, Malawi will also be banned from participating in any football competition organised by Confederation of African Football Association (CAF) for the next two years.
FAM has exhausted all the available funding and it needs at least K62 million to honour the remaining fixtures of the competition, says Nyirenda.