David Frost said the Government would reject such a request as the legally binding June 30 deadline for extending negotiations beyond 2020 looms.
He was responding to a letter from the Westminster leaders of the SNP, Lib Dems, Plaid Cymru, SDLP, Greens and Alliance Party calling for a 24 delay amid deadlock in talks.
Lord Wood of Anfield said during a Lords EU committee hearing this afternoon: “It sounds like the June deadline for an extension request is neither here nor there, it won’t be used under any circumstances. Is that true?
“Are there any circumstances for doing the negotiations that would prompt you to actually consider an extension request?”
Mr Frost responded: “The Government’s position’s pretty clear that we are not going to ask for an extension and if the EU asks for one, we will not agree to that.
“So I think that’s just part of the framework now and we’re working to an end-year deadline."
Earlier this month, the negotiator admitted "very little progress" had been made in the "disappointing" latest round of talks with the EU.
He hit out at the EU's negotiator Michel Barnier, saying he found it "hard to understand why the EU insists on an ideological approach which makes it more difficult to reach a mutually beneficial agreement."
The two sides are at stalemate over trade, security and fisheries ahead of the next round of talks which begin on June 1.
Downing Street has previously said it could be forced to divert its attention from negotiations towards a no-deal scenario if no breakthrough is made by July 1.