While Pakistan and other governments have sought to foster separate talks in recent years, progress has been scant since the 2016 death of Taliban leader Akhtar Mohammad Mansour in a US airstrike.
Obama's considerably lenient military policy also highly restricted the US military advisors from implementing any major strategic decision without the approval from the White House, a limitation which will be rolled back if the new military policy comes into effect.
The plan is yet to be approved by U.S. President Donald Trump.
However, CBS News correspondent Major Garrett says senior administration officials tell him and Brennan the U.S.is much more interested in new methods, new tactics and - they hope - new results against the Taliban than bringing it to the bargaining table.
"They did the exact same thing to ex-President Barack Obama when it came to Afghanistan".
Afghan Ministry of Defense spokesman Gen. Dawlat Waziri said that a troop increase would benefit Afghanistan and the worldwide community. The plan essentially doubles down on supporting the Afghan National Security Forces in the fight against the Taliban.
Trump will reportedly make the final call on the plan before a May 25 meeting with North Atlantic Treaty Organisation heads of state in Brussels.
All are commanded by Nicholson, commander of U.S. Forces Afghanistan and NATO's Resolute Support mission.
There is probably one thing that is pretty clear that he will ll do.
More British troops could be deployed to Afghanistan amid rising fears over security in the troubled country.
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The increase in American troop numbers may be accompanied by a rise in NATO troop levels as well, added the New York Times: "NATO nations would also be asked to send thousands of troops, and the precise number of American forces deployed would probably depend on what those allies were prepared to do".
Nearly sixteen years after the USA -backed ouster of the Taliban, Afghanistan remains in the grip of a war with "shockingly high" death rates among security forces and a record number of casualties among civilians, according to the US government watchdog monitoring the country's reconstruction efforts.
The White House would have to approve the proposals, likely before the next North Atlantic Treaty Organisation meeting on 25 May in Brussels.
"What they are saying behind the scenes is that they don't think they can defeat the Taliban, but they need to try and change the balance; to try and incentivise the Taliban to get to some sort of political solution".
Last month, the Taliban announced the start of their "spring offensive" a week after killing at least 135 soldiers in a military compound. Sgt. Rogers, of Bloomington, Illinois, and Sgt. Cameron H. Thomas, of Kettering, Ohio, were U.S. Army soldiers killed while conducting a joint U.S.
The deteriorating security situation has led Mattis and the White House to give Nicholson more leeway on how and when to use his forces in assisting the Afghan forces.
According to the report, the increase in United States troop level and aid to Afghanistan would be conditioned upon the efforts of the Ghani Government in Kabul to fight against corruption and improve governance.
A request is said to have been made over the past few weeks for the force strength to be increased. The three most recent USA deaths in Afghanistan were in combat last month against the IS affiliate, which also was the target of a much-publicized US airstrike April 13 using the "mother of all bombs".
The NATO meeting this month will be crucial to the next steps by the Trump administration.