International donors have backed the plan, which offers support for those Taliban fighters who come over to the government side.
Al Jazeera's James Bays, reporting from Kabul, said that the comments marked the first time a senior government official had said that fighters were actually coming to talk to the government about changing sides.
But he said that Stanekzai was "worried that if he gave specific geographic areas, specific villages and towns, then the Taliban may focus on those areas and take their revenge on those who had changed sides".
The concerns show the influence that Taliban and other armed groups still wield in Afghanistan, almost nine years after a US-led invasion forced them from power in Kabul.
Plans to bring the so-called moderate Taliban onto the government side were discussed at a peace conference or "jirga" in Kabul, the capital, in June.
The meeting of elders and officials was seen as a national attempt to end the worsening violence and years of war and foreign interference.
The success of the jirga's plan "depends very much on the support of the whole Afghan nation," Stanekzai said.
Al Jazeera's Bays said that "a huge government trust fund," was set-up at that jirga which can be used to buy off the so-called ten-dollar Taliban, who fight because they do not have jobs or income.
Nato countries and their allies say they are trying to find employment alternatives, so low-level fighters can walk-away from the conflict.
The United Nations security council has removed 10 Taliban names from a blacklist of people affiliated with the Taliban in a move some say is designed to convince low-level fighters that they can leave the organisation without sanction.
The peace jirga had asked for the security council move as part of its reconciliation plans.