"We are very clear as a government of the strength of the union… yes there will be some specific factors in Northern Ireland… but it is with that intent, it is with that focus and therefore the concept of special status, I think, is the wrong approach," Brokenshire said.
He said Brexit negotiations would focus on the getting the best possible deal for all parts of the United Kingdom.
Northern Ireland's Alliance party, Social Democratic and Labour Party (SDLP) and Sinn Fein want a deal for Northern Ireland after Brexit to allow the free movement of people and goods across the border.
Alliance party deputy leader Stephen Farry told Sputnik in January that Northern Ireland is already an anomaly based on the Good Friday peace accord and by its geographic location: it is the only part of the United Kingdom that shares a land border with the European Union.
The UK government has stressed that it is committed to working with the people and institutions in the devolved governments of Northern Ireland, Scotland and Wales during Brexit negotiations.