The Haqqani network is described by the US as one of the three main anti-government armed groups operating in Afghanistan, alongside the Taliban and al-Qaeda.
It is thought to be responsible for the most sophisticated attacks in Kabul and across the country.
Al Jazeera's Zeina Khodr, reporting from Kabul, said reports about Karzai's meeting have fuelled increased speculation in the Afghan capital that Pakistan is trying to strike a deal in Afghanistan that would safeguard its interests here.
"With the US war effort floundering and plans by the White House to start withdrawing troops by July 2011, Karzai may be cosying up with Islamabad," she said.
"It may be the reason behind the forced resignations of the Afghan interior minister and intelligence chief who are hard-core opponents of the Taliban."
Haroun Mir, a political analyst, says secret talks are sparking suspicion among Afghans
Our correspondent was referring to the resignations of Amrullah Saleh, the head of the Afghan intelligence, and Hanif Atmar, the interior minister, earlier this month.
"Any political agreement may temporarily find a solution - but giving Pakistan a say in Afghan politics could undermine stability in the long term, especially among Afghans hostile to their neighbour," she said.
Afghan media have also reported that secret meetings are taking place and that Karzai is actively trying to hammer out a deal with groups opposed to his government.
Leon Panetta, the director of the US Central Intelligence Agency, said there was "no evidence" that the Haqqani network leadership was willing to negotiate.
"We have seen no evidence that they are truly interested in reconciliation where they would surrender their arms, where they would denounce al-Qaeda, where they would really try to become part of that society," Panetta said in an interview with ABC News.
"We have seen no evidence of that."
Hekmat Karzai, the director of the Kabul-based Centre for Conflict and Peace Studies and a cousin of the Afghan president, said such talks would be that of a pragmatic leader who understands the realities of Afghanistan and the region.
"The fact [is] that regional players support is needed, particularly Pakistan," he said.
"[But] we aren't clear what transpired so far, so we have to wait to see what comes out of it."
Talat Masood, a defence analyst and former Pakistani army general, agrees that it is necessary to bring Pakistan and Haqqani into negotiations.
"It would greatly help and facilitate a peaceful exit of US and Nato forces if these warlords and Taliban are prepared to undertake negotiations and reach some sort of understanding of power-sharing," he said.
Some analysts say Karzai has already begun taking steps towards that end.
"Without a doubt Amrullah Saleh was not happy with Pakistani politics, and Pakistan considered him an obstacle in the way of them gaining a foothold in Afghanistan," Ahmed Saeedi, a political analyst in Kabul, told Al Jazeera.
"The Pakistanis have always said if you want peace you have to go through us."