The ceasefire offer was reportedly handed to Zalmay Khalilzad, Washington’s envoy for talks with the insurgents, late Wednesday in Qatar, a Persian Gulf Arab country where the Taliban maintain a political office.
Taliban officials familiar with the negotiations on Thursday confirmed that the offer was made to US negotiators in Doha, Presstv Reported.
"It is an offer for a ceasefire either for seven or 10 days," media outlets quoted an unnamed source as saying.
"It has been finalized and given to the Americans. It is going to pave the way for an agreement," the source added.
A second insurgent source, based in Pakistan, also said the offer had been handed to the US.
This came hours after Pakistan's Foreign Minister Shah Mehmood Qureshi said the Taliban had shown "a willingness" to reduce its attacks.
"Today, positive progress has been made, the Taliban have shown their willingness to reduce the violence, which was a demand... it's a step towards the peace agreement," said Qureshi in a video statement.
Islamabad has helped facilitate the talks between the Afghan Taliban and Washington in Qatar.
Pakistan was one of only three countries to recognize the Taliban regime, and its Inter-Services Intelligence (ISI) spy agency stands accused of backing the bloody insurgency in Afghanistan, but Islamabad denies the accusation.
The Taliban and the US had been negotiating the deal for a year, and were on the brink of an announcement in September 2019 when President Donald Trump abruptly declared the process "dead".
Talks were later restarted between the two sides in December in Qatar, but were suspended again following an attack near the Bagram military base in Afghanistan, which is run by the US.
Washington has for weeks been calling on the militants to reduce attacks on US forces, posing it as a condition for resuming formal negotiations on an agreement that would see US troops begin to leave the country after a near two-decade war.
On Saturday, two Americans were killed in a Taliban-claimed bomb blast targeting a US military vehicle in southern Kandahar.
More than 2,400 US service members have been killed in Afghanistan.
Last year was the deadliest in five years for the US in Afghanistan, with 23 American troops killed in the country.
The US invaded the Central Asian country after the September 11, 2001 attacks under the banner of seeking to fight “terror” thousands of kilometers away from its own borders.
The invasion deposed the Taliban, but the group has never ceased its operations across Afghanistan, and has vowed to keep up its attacks until the withdrawal of all US-led forces.
The US began negotiations with the militants under President Donald Trump. The Taliban, however, abandoned the talks, citing lack of resolve on the part of Washington to end the military intervention.