Mervyn Gibson, the county grand chaplain of the Orange Order, reiterated views he expressed in an exclusive interview to UTV earlier this month.
The Parades Commission on Wednesday ruled that Orange bands taking part in the parade on Saturday may only play hymns as it passes a Catholic Church, where disorder has broken out during previous parades.
In the lead up to the parade, the Orange Order said that they had been in conversation with clergy and parishioners at St Patrick's Church, but there has been increasing pressure on the Orange Order to meet with a local residents' group.
Until earlier this year, the Orange Order's policy was not to engage with Sinn Féin-backed groups.
Earlier this month, Rev Gibson had indicated to UTV that he saw "no difficulty" in meeting residents' groups in the lead up to the Ulster Covenant parade.
Rev Gibson has now told the Irish News that conversations with residents could happen in private.
A decision was taken in March this year so that 'flexibility be allowed over engagement at a local level'.
In ruling on the event, the parades watchdog said it was disappointed that there was no direct contact between the parade organisers and local residents in the lead-up to Saturday's event.
The Carrick Hill Residents Group have said they are seeking legal advice after the Parades Commission decision.
Frank Dempsey, chair of Carrick Hill Residents' Group, said they have been left "bewildered" by the ruling.
"We've no objections to the marchers coming down Clifton Street. All we are asking for is respect for our community and respect for our church," added Mr Dempsey.
Meanwhile, Father Michael Sheehan reacted to comments by the Orange Order that on two occasions Frank Dempsey, in his capacity as chairman of the residents group, had been invited to join in their conversations about Ulster Covenant Day, which he declined.
He said he was "sorely disappointed" that confidential conversations between the clergy and parishioners with the Orange Order were publicly divulged.
"It was my hope and understanding that these conversations would ultimately lead to discussions with the residents. It is indeed unfortunate and regrettable that this did not happen," he added.
I would urge the Orange Order to demonstrate the worth of their statement by arranging a meeting with the Carrick Hill residents forthwith to find a solution to the problems that exist as a result of previous difficulties.
SDLP MLA for north Belfast Alban Maginness welcomed the Order's decision to change its policy on talking to residents' groups, but said it remains at a "theoretical stage".
"The residents of Carrick Hill remain open to direct dialogue with the Orange Order in advance of the Ulster Covenant Parade on Saturday," he said.
"Only through genuine, direct engagement between Loyal Orders and residents can we hope to solve the problem of contentious parades and I for one will be only too happy to help facilitate that engagement if it means peace returning to the streets of North Belfast," he added.
Sinn Féin MLA Gerry Kelly said that the talks were an issue of "respect".
"The residents are not saying that they want it (the parade) rerouted, they are not saying that they want to stop this parade, but what they are saying is this is an issue of mutual respect," Mr Kelly told UTV.
"I understand why he's trying to bring it down to the chapel, but it actually is wider than the chapel, it is that full route from the Orange Lodge right down past the chapel which counts."
Commenting on the possibility of any future talks, DUP deputy leader Nigel Dodds said that dialogue had addressed the issue of respect surrounding the parade.
Let's not have any idea that just dialogue will solve these problems, we've got to address the issues, and this issue, the issue of respect- the matter was addressed.
Despite the row over the Order's engagement with the local community, there have been united calls for calm ahead of the event.
Tens of thousands of Orangemen and their supporters are expected in the city for the march on Saturday to mark the 100th anniversary of the signing of the Ulster Covenant.
The centre piece of the Covenant commemorations will see a cultural festival staged in the grounds at Stormont.
A maximum of 14 bands and around 1,500 marchers will pass St Patrick's Church on their way to Stormont as they mark the 100th anniversary of the signing of the Ulster Covenant.
The Parades Commission ruled that no loyalist supporters should accompany the feeder parade and bands accompanying Orangemen are only permitted to play hymns, if no church services are taking place.