Published Wednesday, 10 November 2010
Mr Ervine was speaking after calls for such a move - including from the UVF's founder Gusty Spence, in a statement to a BBC Spotlight documentary.
"All we can do is offer an alternative. All we can do is point a way out of the morass to provide pathways of peace into politics, into culture," Mr Ervine said.
"We have been going down that road now for a number of years and we would be delighted if the UVF came along that road with us. I believe that is only a matter of time before that happens."
I believe that leadership are listening. I believe there may well be a sea-change very soon.
Brian Ervine on UTV Live Tonight.
He added: "Gusty's statement to disband presents three questions. Where do the UVF go? When do they go and how do they go? I hope they don't go as looked upon and loathed by their own community."
But journalist Brian Rowan says he is not sure whether the UVF is capable of leaving the stage.
"I'm not sure if the leadership has the authority to order the organisation off the stage," he told UTV. "And I think, whatever happens, there will be those who will remain under the UVF banner and involved in activities which make a mockery of the endgame statement of 2007."
Three years ago, the organisation renounced violence and committed to a process of transformation from a paramilitary to a civilian organisation. In 2009 the UVF also took the step of full decommissioning.
The calls for the organisation to disband come in the wake of the murder of Bobby Moffett on the Shankill Road in May, which the Independent Monitoring Commission said was sanctioned by the UVF leadership but did not break the terms of their 1994 ceasefire.
UVF members are also believed to have been involved in two nights of serious rioting in Newtownabbey last month, when a gunman was spotted on the streets. According to sources, police are also investigating a UVF link to pipe bomb attacks in west Belfast last week.
The incidents have left the Progressive Unionist Party, which is broadly regarded as being politically linked to both the UVF and Red Hand Commando, in turmoil.
But community worker Raymond McCord has said the calls for peace will only fall "on deaf ears".
"These calls don't mean anything to these terrorists and drug dealers", Mr McCord from support group HELP - whose son, Raymond Jnr, was murdered by the UVF - told UTV.
"It's about money and power and terrorising the community."