James Bays, Al Jazeera's correspondent in Kabul, said: "The plan is to widen these talks and to bring in elements of the Taliban."
It is not clear whether the secret negotiations were aimed at separating Hekmatyar's Taliban-linked faction from the group, or encouraging some elements of the Taliban to join the political process.
Michael Griffin, an Afghanistan expert, told Al Jazeera: "If Hekmatyar is in this only to trade for his own survival and immunity from prosecution and eventual retirement, that doesn't provide for his followers.
"If they are not included in the deal, they will follow the Taliban."
Patricia Degennaro, a professor at the Centre for Global Affairs at New York University, told Al Jazeera the talks were a central part of attempts to end the conflict.
"It's long overdue that there is some kind of jirga, or regional council in Afghanistan, where some of these parties who have had grievances over the years are brought together.
"They need to start talking to each other and move forward so people can start putting their arms down."
Divide and rule
Mullah Mottawakil, a former Taliban foreign minister, said the talks would fail if the plan was to split the Taliban.
"It will not benefit anyone if he [Hamid Karzai, the Afghan president] brings one part of the Taliban into the government, and leaves the other part behind. It will not finish the war."
Ghairat Baheer, one of Hektmatyar's two son-in-laws released from the US prison at Bagram airbase in Afghanistan in May last year after six years in custody, is involved in the process, according to reports.
Baheer, an ambassador to Pakistan in the 1990s, was given a visa to travel to London by British authorities last month.
Humayun Jarir, a Kabul-based politician and son-in-law of Hekmatyar, is also said to have been involved.
Karzai has long proposed holding talks with the Taliban.
Should secret talks be taking place without his knowledge, it is likely to undermine him and further sour relations between the US and Afghanistan, Bays said.
There have been other attempts to open talks between the Afghan government and Taliban representatives in recent months, Al Jazeera has also learned.
|Humayun Jarir, Hekmatyar's son-in-law, is purported to be involved in the talks
Ahmed Jan, an intermediary for the Taliban and tribal elder from Helmand province, was sent on behalf of the Taliban to Kabul for talks with the Afghan government last year, Bays said.
Jan was arrested after US officials discovered the talks were to take place, and is in US custody at Bagram, an Afghan political source told Al Jazeera.
With the arrival in Kabul last month of Richard Holbrooke, the US envoy to Afghanistan and Pakistan, resistance to the idea of holding talks with the Taliban may change, Bays said.
Ahmadshah Ahmadzai, another former Afghan prime minister, said trying to bring all Afghan parties – including Mullah Omar, the Taliban leader - to the negotiating table is the only option.
"If Mullah Omar agrees [to talks] and those around him do - this is the real Taliban faction - then they can bring peace."
Degennaro said: "It's really important to at least test the waters and see what's happening, and what response we're going to get, which is probably what they're doing right now."
The Afghan foreign minister is currently in Washington DC to discuss the future of the region.