The United States, the largest contributor in terms of manpower and money by far, is expected to ask alliance members to shoulder a quarter of the costs of supporting Afghan forces.
The total cost is expected to total around $4 billion a year, with the U.S. looking to pay $3 billion.
The meeting comes just a few days after militants severely tested Afghan forces with a wave of bombings and attacks across the country.
On Sunday, over 38 militants and eight Afghan security forces were reportedly killed after an 18-hour battle with insurgents in the capital of Kabul and in other provinces across the country.
Foreign embassies, NATO headquarters and the Afghan parliament were hit by a series of attacks initiated by either Taliban insurgents or Haqqani fighters on Sunday -- the first major assault on an Afghan city in more than six months, and one of the most serious since U.S.-backed Afghan forces removed the Taliban from power in 2001.
On Monday, Afghan President Hamid Karzai swiftly condemned NATO for intelligence failures, blaming the alliance for not forewarning Afghan security forces of the attacks.
However, on Tuesday, Karzai called on the U.S. to pledge a minimum of $2 billion towards maintaining Afghan security after the alliance's departure.
NATO leaders have also insisted that the 2014 withdrawal strategy remain unchanged despite the attacks.
Wednesday's talks are aimed at preparing the ground for a summit of NATO heads of state in Chicago next month, where a final decision on the funding is expected.