Councillors gave their reaction after recent speculation on the issue, and in light of DUP Minister Sammy Wilson's comments at the weekend calling for an end to what he called "inter-Unionist division".
While some Ulster Unionist party councillors were reluctant to speak out on the issue without party consultation, members of the DUP largely agreed with the Finance Minister's comments.
Long-standing councillor Jim McElroy said the formation of one Unionist party for Northern Ireland is something he has always argued for.
"I think it would be ideal if all the Unionist factions came together - in fact, I have always said this," said Mr McElroy.
"I think we need an electoral pact at least to put Unionism in a stronger position."
election
Dromore councillor Paul Rankin said the idea of one Unionist party is a long way away but welcomed plans for Unionist parties to work together at election time.
"I think we need to take small steps," he said.
"I cant imagine us forming one party in the short-term but I wouldn't rule out the UUP and DUP working more closely together in the future.
"I think the one thing we can say we have in common is we are both pro-devolution parties who want to move forward."
Councillor Norah Beare, who defected from the UUP to the DUP some time ago, said she had not given the issue much thought but feels it makes sense.
She said, "If we are all supposed to be singing from the same hymn sheet as such then I can see that it might be a good idea."
However UUP branch chairperson Joan Baird said she would not be keen to comment until she consulted with fellow party members.
She said, "At the minute people within the party are very concerned and really just want to be given more information on the whole situation."
TUV Councillor Stephen Herron said, "Many Ulster Unionists, I believe, will be wary of the self-preservation motivation which drives the DUP's new found bonhomie towards the party which they hitherto vilified at every turn."
Other Unionist councillors were unavailable for comment.