The US is preparing to withdraw thousands of troops from Afghanistan in exchange for concessions from the Taliban, including a ceasefire and the renunciation of Al Qaeda.
The agreement would require the Taliban to start negotiating a larger peace deal with the Afghan government, The Washington Post reported.
It could decrease the number of US troops in the country from 14,000 to between 8,000 and 9,000, which is a similar amount to when President Donald Trump took office in January 2017.
The Trump administration has had eight rounds of negotiations with the Taliban, which controlled Afghanistan between 1996 and 2001.
The talks have been led by envoy Zalmay Khalilzad, the Afghan-born former US ambassador to Kabul.
"If the Taliban do their part we will do ours and conclude the agreement we have been working on," Mr Khalilzad tweeted on Wednesday.
"I am wrapping up my most productive visit to Afghanistan since I took this job as special rep."
Officials said the agreement could be secured before the Afghan presidential election in September, although they said this could be delayed by Taliban leaders.
If the deal is approved, it would be a significant step towards ending an 18-year war – America’s longest and most expensive conflict.
"I would say that they are 80 or 90 per cent of the way there," a US official told the Post. "But there is still a long way to go on that last 10 or 20 per cent."
Taliban spokesman Zabiullah Mujahid declined to comment about the likelihood of an initial agreement.
In recent months, the size of Afghanistan’s National Defence force has been dramatically reduced because of a bid by the US to stamp out “ghost” soldiers – fake names on payrolls.
Meanwhile, a report that came out on Tuesday said the State Department wasted $103 million (Dh378.3m) to build a security compound in Afghanistan before abandoning the project after it barely took off.