The treasury chief Alhaj Mohammad Aqa told Reuters that the previous two attempts to sell the loss-making bank failed to find a suitable buyer.
The original Kabul Bank collapsed in 2010, reeling with debts of almost $1bn, which led to a financial crisis.
According to Aqa, over the past four years the troubled bank has lost around $56m owing to stringent rules on its lending and investment.
The news agency quoted Aqa saying that initially the authorities planned to merge three public banks – Pashtany Bank, Bank-e-Millie and New Kabul Bank.
Even though IMF confirmed the talks, it did not reveal when it will decide on a plan.
IMF said it is in the process of evaluating options with the government and the central bank regarding state banks, including New Kabul Bank.
The bank is under the supervision of Da Afghanistan Bank (DAB), the central bank of Afghanistan.