Three loyalist paramilitary groups have reportedly started to decommission their weapons.
It is understood the Ulster Volunteer Force (UVF) made a significant handover a few days ago, with further disarmament moves by the Ulster Defence Association (UDA) and Red Hand Commando (RHC).
Both the UVF and UDA have been under pressure for some time to begin dumping their guns following the IRA's decision to dispose of their weapons four years ago.
It is understood General John de Chastelain, head of the decommissioning body, is in Belfast and has met senior loyalists.
Deadline
A spokesman for the Independent International Commission on Decommissioning (IICD) said: "We have no comment at this stage other than we expect to be reporting to the government at the end of August."
Northern Ireland Secretary Mr Woodward said on Thursday night: "If these reports were to be confirmed, what we would see would be a seismic transformation within loyalism."
Earlier this year Mr Woodward controversially extended legislation allowing paramilitary groups to decommission in the hope loyalists would fully engage with the IICD.
But he warned that if the loyalists did not act by August, he would be closing down the process.
Our Political Editor Ken Reid, who broke the story to Frank Mitchell on U105, said: "In the past week, loyalist paramilitaries have started decommissioning their weapons."
He said that much discussion had taken place over the past few months between the mainstream unionist parties, the British government, and the paramilitaries.
"I think that the intention would be that it would be completed during the course of the summer - maybe as early as July.
"My understanding is that the process has started."
Discussions
First Minister Peter Robinson said: "Over the last nine months the DUP has been engaged in ongoing discussions with both the UDA and UVF leaderships."
"The objective of the discussions has been to assist the organisations' transformation from paramilitary organisations into people who are playing their full part in a peaceful and democratic Northern Ireland with violence and criminality being firmly a thing of the past," he said.
"Part of this process is ensuring the organisations wind down their paramilitary structures and decommission their weaponry."
He said that the DUP was aware of the organisations' engagement with the Independent International Commission on Decommissioning.
The leader of the UVF-linked Progressive Unionist Party, Dawn Purvis, was unable to confirm decommissioning had taken place.
But she said that loyalists had been involved in ongoing contacts with the IICD.
"That is to be welcomed," she said. "That is where the process of decommissioning has to be dealt with."
Ulster Unionist Party leader Sir Reg Empey said: "This is something that we have been working on for the last few years and it shows the progress that Northern Ireland has made."
'Significant'
Alliance Leader David Ford said: "This appears to be a significant development. Progress from loyalist paramilitaries was needed and I hope there can be swift and full decommissioning.
"For decades, paramilitary groups from both sides have held communities in their grip of fear. I hope that this move will lead to the end, not simply another endgame."
Senior Sinn Fein representative Gerry Kelly said: "The IRA dealt with the issue of arms in a decisive way four years ago.
"If these reports prove to be true and the UVF have now followed suit then that would obviously be a welcome move.
Chief constable Sir Hugh Orde also hailed loyalist decommissioning as "very good news".
Sir Hugh said: "They are to be congratulated for taking that big leap. I think it is very significant.
"I think it is a step change which shows a degree of organisation and commitment that perhaps we have not seen before."
Barry Gilligan, chairman of the Northern Ireland Policing Board, said he had not been formally informed of decommissioning, but said: "If that is the case, the board welcomes it.
"Any day that sees the removal of weapons from our community is a very significant day and this board welcomes it."
Taoiseach Brian Cowen also welcomed the reports and said he looked forward to official confirmation.
© Press Association