Military leaders would also regain the authority to target Taliban leaders with airstrikes under the proposals, BBC reported on Tuesday.
President Donald Trump has not approved the plan, unnamed officials said. It may include a request that other NATO countries send 3,000-5,000 soldiers.
There are 13,000 NATO troops currently in the country, 8,400 of them US.
US combat operations against the Taliban officially ended in 2014, but Special Forces have continued to provide support to Afghan troops.
In February, the commander of US troops in Afghanistan, General John Nicholson, told a Senate committee there was "a shortfall of a few thousand".
He said he needed more troops to break a "stalemate".
Last month, the Taliban announced the start of their "spring offensive" a week after killing at least 135 Afghan soldiers in a military compound near the northern city of Mazar-i-Sharif.
The group said it would use military alongside political tactics and that its main target would be foreign forces.
On Saturday Taliban terrorists seized a district just a few kilometers to the west of Kunduz in their continuing attempts to take the northern city. Thousands of families have been forced to leave their homes.
Latest reports suggested the Taliban now also control the main road to the east of the city which links the province to the northeast and is also the main supply route for the capital, Kabul.
Another Taliban assault on the strategic stronghold is under way, the first major operation of the "spring offensive" the group announced two weeks ago.
In March, Taliban retook the key district of Sangin in the southern province of Helmand, consolidating their already tight grip on a region hundreds of British and US troops died trying to protect.
The Taliban are now reckoned to control up to a third of the entire country. Indeed, the big question is whether a few thousand additional foreign troops will be enough to turn the tide.
US officials said the new plan would significantly expand the combat role for US troops, and authorize the Pentagon, not the White House, to set troop numbers.
President Trump is expected to make a decision before he attends a NATO summit in Brussels on May 25.
Former US president Barack Obama set deadlines for cutting the numbers of US soldiers in the country and removed the Pentagon's authority to directly target Taliban leadership.
However, he was forced to abandon the troop reduction target.