Both the DUP and Ulster Unionists have signalled that an electoral pact involving the two parties is unlikely to happen.
The party leaders held "business-like" discussions on Monday but there has been no further engagement since.
The news will come as a disappointment to the Orange Order, which yesterday issued a statement saying it was "incumbent on our unionist leaders and representatives to cooperate and coalesce".
Both parties have already made unilateral gestures, with the Ulster Unionists choosing not to field candidates in North Belfast, West Belfast and Foyle, while the DUP has said it will not contest Fermanagh and South Tyrone.
Further discussions were expected in relation to East Belfast, South Belfast and South Antrim but it now appears enthusiasm for a pact is waning on both sides.
There was a setback in relations between Arlene Foster and her newly-appointed Ulster Unionist counterpart Robin Swann before negotiations had begun when the DUP leader said her party wanted a clear run in South Belfast in exchange for standing aside in Fermanagh and South Tyrone.
Mr Swann accused the former first minister of arrogance and said her remarks made agreement more difficult.
Both parties confirmed yesterday that there were currently no plans to hold further discussions.
Nominations for the June 8 election close on Thursday May 11.
In its statement, the Orange Order's Grand Lodge said the forthcoming Westminster election was of "critical importance and huge significance".
It said a stable British government was essential with Brexit looming, as was the need for the north to have a strong voice at Westminster.
The order said its membership's "broad range of political opinion" meant it welcomed closer collaboration between pro-union parties.
"We believe it is in Northern Ireland’s vital interests for as many unionist MPs as possible be returned to our mother parliament," the statement said..
"In order to maximise the pro-union vote in this election it is incumbent on our unionist leaders and representatives to cooperate and coalesce, parking party interests and acting in the best interests of the union."
The Grand Lodge said strategic thinking and cooperation was all the more crucial at a time when republicanism was "buoyant following its recent electoral success".
"Republicans simply do not care if Northern Ireland succeeds as an integral part of the United Kingdom. – the opportunity to answer their united Ireland agenda and insatiable demands will occur on 8 June," the statement said.
"The onus more than ever is on Unionism to come together, selling its collective ideals to the widest possible audience."
The order said it would continue to seek to accommodate unionist unity.
