The order says negotiations as part of what it calls the Twaddell Initiative will only start after Orangemen complete their return parade past the Ardoyne shops.
Violence erupted in Belfast and other parts of Northern Ireland after three Ligoniel Lodges were barred by the parades watchdog from making the return journey past the area on the Twelfth of July.
The Order has since held a number of protest parades to police lines along the Woodvale Road.
Supporters of the bands have also set up a protest camp on Twaddell Avenue and say they will not leave until the return leg of the Twelfth parade is allowed to pass.
On Sunday, the Orange Order released a statement saying it was to apply for another parade past the Ardoyne shops at an alternative time in a bid to allow the lodges to "return home".
The Order said it will apply for the three lodges and two bands to march at 9am on Saturday 5 October.
The organisation said it wanted to contribute to the current "positive atmosphere" brought by the Haass talks and called for "tolerance" from Ardoyne residents.
It also said it was committed to "full and open" dialogue with residents for next year's parade which could begin "immediately after our return to Ligoniel Orange Hall".
We call on all involved in seeking a solution to this issue, to match our determination to achieve an equitable resolution.
The Orange Order and some Ardoyne residents had engaged in short-lived talks ahead of the annual parade last July.
The Orange Order said: "This Initiative emanates from all such dialogue and takes cognisance of the views expressed by residents. It is made without prejudice to future engagement.
"We believe the time is right to launch this initiative to resolve the present impasse and address the unique situation that the Parades Commission determination created at Woodvale."
"We are also conscious that the issue of parades, flags and the past are to be the subject of intensive and ongoing political discussion.
"We wish to contribute to a positive atmosphere for the Haass talks and assist them to reach a successful conclusion.
"This Initiative makes a clear commitment to future dialogue to ensure we do not find ourselves in a similar situation in 2014."
Unionist politicians have welcomed the move.
First Minister Peter Robinson said the onus was on nationalism to "show leadership".
The commitment and foresight of the offer of dialogue for 2014 is to be welcomed.
Peter Robinson, DUP
The DUP leader said: "I commend the lodges and bands for launching this Twaddell initiative to resolve the situation.
"It has the full support of the DUP and its local elected representatives."
He went on: "The Parades Commission has failed to give due recognition to the dialogue in July this year and in previous years.
"Now they have the opportunity to do so.
"The onus is now upon nationalism to show leadership and to respond positively to this genuine attempt to reach accommodation.
"They must face down the elements in their community who wish to drag Northern Ireland back.
"The act of sharing a main arterial route for a few minutes would boost community relations in north Belfast significantly and generate a positive atmosphere for the Haass process," he added.
Ulster Unionist leader Mike Nesbitt said: "Having a 2013 parade stuck incomplete does nothing to help."
"I have called for some time for a spirit of generosity to be shown by all. This may open to the door to such a game-changing attitude," he added.
Meanwhile PUP leader Billy Hutchinson applauded "those involved in this initiative for making the clear commitment to future dialogue well in advance of next year's Twelfth of July celebrations".
"I think in light of this announcement, the sensible option is for the parade to be allowed to pass peacefully in the next week, providing up to forty weeks for dialogue between all involved before next year's demonstration," he added.
In September American ambassador Dr Richard Haass opened talks with political parties and other interested groups.
The independent chair was invited by the First and Deputy First Ministers to hold talks in a bid to help resolve issues surrounding parades, flags and the past.