Negotiations are believed to be progressing after high-level talks last month ended with a "draft framework" on potential US troop withdrawal and a pact to prevent Afghanistan from harbouring terrorists.
The US has also pushed for a ceasefire and the opening of a dialogue between the Taliban and the Kabul government — demands that have been repeatedly rejected by the insurgents.
"All American troops would withdraw from Afghanistan over the next three to five years under a new Pentagon plan being offered in peace negotiations that could lead to a government in Kabul that shares power with the Taliban," read the report published Thursday.
The newspaper said more than half a dozen current and former American and European officials had described aspects of the plan that could see US troops levels cut by half in the coming months and "largely shift American operations to counter terrorism strikes".
US, Taliban talk troop withdrawal, counter-terrorism at peace talks
There are approximately 14,000 US troops based in the country, providing training and air support to Afghan forces along with overseeing counterterrorism operations.
Thousands of European and international troops also assist in the training mission.
The Taliban were quick to reject the New York Times claims, saying they were unaware of any such proposals made during the months-long diplomatic push.
The publication of the report comes as the US and Taliban have temporarily paused peace talks in Doha, with negotiations set to resume over the weekend.
"No talks have been held in the meetings regarding an interim government and elections, nor has the US side proposed anything regarding staying in Afghanistan for four or five more years," said the Taliban in a statement Friday.
Current talks had "solely revolved around withdrawal of foreign forces and the nature of this pullout as well as nature of assurances regarding future Afghanistan," it added.
The Afghan government and civil society groups have voiced concerns that an abrupt US withdrawal could spark an even bloodier civil war or a return of hardline Taliban rule.
Meanwhile, violence has flared, with the Taliban claiming a pre-dawn strike on a US-Afghan base in the southwestern province of Helmand.
At least four militants were killed, provincial and defence officials said Friday, after insurgents gained access to the base sparking heavy firefights with Afghan forces.
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