DUP chief whip Sir Jeffrey Donaldson has dismissed the notion the DUP's influence on the Government is "waning" and than the Government is seeking a Northern Ireland-only backstop.
His comments come as Number 10 has announced that Prime Minister Boris Johnson would meet the DUP's Arlene Foster and Nigel Dodds in Downing Street on Tuesday afternoon.
The Prime Minister's official spokesman told a Westminster briefing that he expected the meeting to include discussion on a "range of subjects including Brexit".
Sir Jeffrey told BBC Radio 4's World at One programme: "I don't see the Prime Minister who appointed himself as the minister for the Union agreeing to an arrangement that separates Northern Ireland from Great Britain in trading terms.
"So, I think that this idea that you have a Northern Ireland-only backstop where you have a trade border in the Irish Sea between Northern Ireland and Great Britain is simply a non-runner, in any event it would contravene the core principles of the Good Friday Agreement, the Belfast Agreement."
He added: "The solution to avoiding a hard border on the island of Ireland is not to create a second border in the Irish Sea because I think that would be deeply destabilising."
Sir Jeffrey said a considerable number of Tory MPs would look to the DUP to see what its view was on any arrangements relating specifically to Northern Ireland.
He said: "The idea that our influence is waning, I think, flies in the face of reality. Our leader will be meeting with Boris Johnson, we are plugged into the ongoing discussions about alternative arrangements, we have a significant role to play and, therefore, I would argue that our influence remains."
