Washington (CNN) -- As many as 2,000 additional troops -- including a number of U.S. forces -- may be headed to Afghanistan in the coming weeks under a plan backed by Gen. David Petraeus, CNN has learned.

Petraeus has not commented publicly on the need for more troops, but a U.S. defense official and a senior NATO official directly familiar with his thinking and the entire matter have confirmed details to CNN.

The proposal for more troops has been briefed to NATO officials behind closed doors.

According to the NATO source, it calls for an additional 2,000 troops including at least 750 personnel to serve as trainers for Afghan forces. The trainers specifically would work to teach Afghan units how to support their operations in the field. The balance of the forces would work largely to counter the still significant threat posed by improvised explosive devices (IEDs).

Another NATO official tells CNN "it's highly likely" many of the additional forces will be U.S. troops. Some NATO member countries are politically ambivalent about the war, he noted. And practically, it is only U.S. forces that have the most advanced equipment to counter roadside bombs

In May, Defense Secretary Robert Gates sent 850 U.S. military trainers on a temporary deployment when European countries could not pledge enough of their own forces. This latest need for 2,000 forces goes beyond that to include counter-IED forces, although some small number of the at least 750 additional trainers could replace those already there.

No final decisions have been made on any additional U.S. troops.

NATO military authorities are scheduled to meet in the coming days to try to get specific troop commitments from member nations. The goal is to get the matter resolved before a November NATO summit in which U.S. and NATO military commanders are expected to discuss progress in the war.

It is not clear whether the new effort will bring the troop levels above the 30,000 additional U.S. forces authorized by President Barack Obama earlier this year, as it will depend on how many troops the NATO countries contribute and the potential re-assignment of existing forces. The president also authorized the Pentagon at the time to deploy 3,000 forces, but more than half of those 3,000 have already been earmarked.

NATO sources emphasize they believe the bulk of the additional 2,000 will likely have to come from the US.

The potential for yet another troop increase, even a relatively small one, is already being defended by NATO. The senior official told CNN "this relatively small uplift -- less than 2 percent of the 150,000 in theatre from the coalition -- reflects the direction of the campaign: training the Afghan security forces to prepare for transition, as well as protecting our forces."

A U.S. military official also confirms that in recent weeks the discussion of the "withdrawal" of forces from certain areas of Afghanistan beginning in July 2011 has taken a bit of a twist.