Under the proposed draft the US would withdraw some 5,000 troops from Afghanistan - with TIME Magazine reporting that number could be as high as 5,400 - and shutter five bases within 135 days.
Additionally, the deal would require the Taliban commit to not allowing Afghanistan to be used as a base from which militant groups, such as the Islamic State or Al Qaeda, could plan attacks on the US and its allies.
Throughout the negotiations Taliban officials insisted that all foreign forces must leave the country, which has fuelled concerns that if the US were to fully withdraw it would leave the US-backed government of Afghanistan vulnerable, especially with its security forces already stretched thin, mired in allegations of corruption and suffering losses.
Pompeo might be having issues with the deal as it does not ensure several crucial things, those familiar with the discussions told the magazine. It does not guarantee the continued presence of US counter terrorism forces to battle Al Qaeda, the survival of the pro-US government in Kabul, or even an end to the fighting in Afghanistan.
"That may explain why Pompeo is declining to put his name on the deal," according to the report, which cited senior American, Afghan and European officials.
The report said that Pompeo was asked by the Taliban to sign an agreement with the Islamic Emirate of Afghanistan - the name of the government founded by the Taliban in 1996 until its ouster in 2001 - which would put the Secretary of State in the position of officially recognizing the Taliban as a legitimate political entity, rather than an insurgency.
Ironically, the Taliban's push for international recognition of its "Emirate" blew up any chance of peace negotiations back in 2013.
Still, Pompeo's apparent reluctance to sign on the dotted line doesn't mean a deal was totally dead.
According to TIME, chief US negotiator Zalmay Khalilzad could just sign it himself, or Washington and Taliban may issue a joint statement supported by the Kabul government and other countries.
Pompeo's office declined to comment before publication of this story. After it was published, Pompeo said through a spokesperson that he might sign if US President Donald Trump and all parties struck a deal.
"There is no agreement to sign yet. If and when there is an agreement that is approved by all parties, including President Trump and if the Secretary is the appropriate signatory, he will sign it," State Department spokesperson Morgan Ortagus emailed TIME.
US military and intelligence officers and diplomats who served in Afghanistan worry that once a withdrawal is underway, it will be irreversible, given Trump's promise to end the US involvement in the war there, the fast-approaching 2020 US elections and the absence of public support for the war.
The price of peace, they fear, might include reversing much of the hard-won progress towards building a stable country over nearly two decades of war.
( With inputs from IANS )