Loyalist leader Billy Hutchinson says any new parades initiative will only be worthwhile if there is a compromise with the loyalist community.
The Belfast councillor and PUP leader was speaking days after the meeting between the combined unionist leadership and the Secretary of State.
A Sinn Fein delegation also met Theresa Villiers last Tuesday – part of talks over the year-long marching standoff in north Belfast.
"She [Ms Villiers] might do something but it depends on what it is," Mr Hutchinson told the Belfast Telegraph.
"It will only be worthwhile if it helps resolve the issue. It has to recognise culture. There has to be some compromise."
The councillor attended last Tuesday's meeting with a unionist delegation including First Minister Peter Robinson and Ulster Unionist leader Mike Nesbitt.
"This is her [Ms Villier's] opportunity to deal with the issue and to make sure that we can deal with the rest of the past," Mr Hutchinson said.
Observers believe Ms Villiers is considering an initiative, but stress it must not undermine the Parades Commission.