Afghan police currently number about 80,000
The US is planning to more than double Afghanistan's national security forces to try to bring stability to the country, the New York Times reports.
It quoted senior US administration officials as saying the plan would mean creating a force of about 400,000 Afghan troops and police officers.
President Barack Obama is currently finalising a new strategy for the war against the Taleban.
He has set Afghanistan as a foreign policy priority.
The New York Times said the president was expected to approve the new plans for Afghanistan in the next few days.
However. it said there were already concerns about the cost of boosting the army and police - which it put in the range of $10bn to $20bn over the next six or seven years.
The new plan would increase the army to about 260,000 soldiers, with the remainder made up of police, border guards and commandos, the paper quoted officials as saying.
It said there were concerns about such a large force given what it called the corruption in the Afghan government, but said officials believed the Taleban insurgency was the greater threat.
Defence Secretary Robert Gates has not commented in detail on the new strategy.
However he said: "I've been very concerned about an open-ended commitment of increasing numbers of troops for a variety of reasons, including the size of our footprint in Afghanistan and my worry that the Afghans come to see us as not their partners and allies, but as part of their problem."
Reuters news agency quoted a US official as saying another part of the new strategy would be a "civilian surge" in which hundreds of US civilian officials would be deployed nationwide to try to counter the effects of the insurgency.
One key issue the new strategy will have to tackle is whether to increase drone missile strikes inside Pakistan.
The US has stepped up such attacks this year but the Pakistani government regularly expresses anger, saying they are a violation of its sovereignty and breed local resentment.
The New York Times had earlier reported that the US was considering expanding strikes into Balochistan province.