Speaking after meeting British Prime Minister Theresa May in the UK capital, London, on Wednesday, Stoltenberg insisted this would not mean a return to combat operations.
"We have received a request from our military authorities to increase our military presence in Afghanistan with a few thousand troops," he said.
"It will continue to be a train, assist and advise operation," Stoltenberg added.
"We are now looking into requests regarding some areas like more education, for the military academies, but also training special operation forces and air forces."
The issue will be high on the agenda at the NATO annual summit in Brussels on May 25.
Since NATO's combat mission in Afghanistan formally ended in 2014, Taliban attacks have intensified and Afghan military and civilian casualties have risen.
NATO already has some 13,450 troops in Afghanistan, including around 6,900 US and 500 British military personnel, who are training the Afghan armed forces to eventually take over the country's defence and security. The US has an additional 1,500 soldiers conducting assist missions directly under Pentagon command.
"The implication is that the Afghan army simply does not have the edge when it comes to the tackling of the Taliban going forward," Al Jazeera's Neave Barker, reporting from London, said.
Stoltenberg's visit to the UK came a day after reports suggested NATO had asked Britain for more troops a few weeks ago.
Separately, the US administration is reportedly considering deploying more troops to Afghanistan as well. Official sources quoted anonymously by US media said the increase would range from between 3,000 to 5,000 soldiers, including Special Operations forces.
President Donald Trump is expected to receive a proposed new approach to the war this week, according to Theresa Whelan, a Pentagon policy official.
"This isn't the first and this isn't the last NATO alliance member that Stoltenberg will travel to but we will not have a fuller sense of the kind of troop levels, and the kind of commitments made by alliance members until the leaders' summit at NATO headquarters on May 25", Barker added from London.
Afghanistan has seen intensified Taliban attacks across the country, leaving Afghan forces - already beset by killings, desertions and vacuums in leadership and morale - stretched on multiple fronts.
They have faced high casualties, up 35 percent in 2016 with 6,800 soldiers and police killed, according to a US watchdog.
According to the United Nations, 583,000 people have fled their homes as a result of the conflict in 2016, the highest number of displacements since records began in 2008.
Source: Al Jazeera and news agencies