Tony Blair's former chief of staff, Jonathan Powell, is also understood to have been involved in the talks.
It is believed a statement is planned for next Tuesday, on the 21st anniversary of the loyalist ceasefire.
On 13 October 1994, the UDA, UVF and Red Hand Commando announced they would "cease all operational hostilities".
Who are the UDA?
Who are the UVF?
Mr McNarry is understood to have been talking to the leadership of loyalist groups for a long time.
The BBC has so far been unable to contact the UKIP MLA to discuss the initiative.
On Tuesday, the News Letter reported comments attributed to a section of the UDA, stating that it still exists and suggesting that it has no intention of disappearing.
It quoted The Loyalist magazine as saying: "We will wait and see which way it pans out, but rest assured the UDA are still in existence and won't be leaving any stage whilst republicans of any faction still exist."
The magazine is said to represent the views of the South Belfast UDA and its political advisory body the Ulster Political Research Group.
UKIP MLA David McNarry is part of an initiative exploring how loyalist paramilitary groups might eventually disband, according to Stormont sources.