Portadown Orangemen have said they are prepared to meet face-to-face with the Garvaghy Road Residents Coalition to try to resolve the Drumcree dispute.
Parades at Drumcree have been peaceful for the past three years
They have also accused the Parades Commission of failing to deliver on a mediation process.
District Master Darryl Hewitt told the BBC they would hold talks with the residents to argue for a parade down the mainly nationalist Garvaghy Road.
Mr Hewitt said the Parades Commission had been told this in October.
"The precondition is that there must be an independent chair (for the talks)," Mr Hewitt said.
"I hope that it leads to a process being instigated where the Garvaghy Road problem can be resolved."
Since 1998, the homeward route of the Orange Order parade has been blocked by the security forces, following a determination by the Parades Commission.
The parade has been marked by serious violence in the past, but it has passed off peacefully in the last three years.
The Parades Commission was set up in 1997 to make decisions on whether controversial parades should be restricted.