Northern Ireland's political parties have until the end of Monday to reach a power sharing agreement; otherwise Westminster will impose a budget.
Jim Shannon told Premier the critical issue is the Irish Language Act proposed by DUP rival party Sinn Fein.
Mr Shannon said it was an "impossible request".
He told Premier: "If someone wants their child at school and wants their child to speak the Irish language, that power within that act means that school, even if it's only one person, will have to have a classroom, book work and appropriate time. There will be costs of course to the government department."
He added that the "powerful" act would mean that street signs would have to be written in Irish and 10 per cent of all people that apply for Civil Service jobs must speak the Irish language. Shannon said these are all unfair rules.
He told Premier: "There are many people in my constituency which have an interest in it and don't see it as a problem, but the Irish language act gives them the authority to do things above and beyond any other language act would have."
Sinn Fein's Conor Murphy said while he believed a deal could still be done, it "needs to be a deal for all in our society and not just for the political leaderships of unionism".
Mr Shannon said although it will be unfortunate if an agreement isn't reached, at least other important issues will be addressed if there's direct rule from Westminster.
He told Premier: "It's not the ideal situation. We would wish to see an accountable regional assembly, like we do have. We want to see it working. We want to see issues of education, health and roads addressed."
The last period of direct rule from Westminster ended in 2007 with Sinn Fein and the DUP's historic deal to head up a new coalition government.
Listen to Jim Shannon speaking with Premier's Tola Mbakwe:
