Dominic Raab told the BBC it was likely the talks were entering the “last real major week”, and an agreement remained possible if the EU showed “pragmatism”.
He added that the talks now depended on resolving a “fairly narrow” set of issues, including fishing rights.
Negotiators are racing to reach a deal, with a looming deadline in four weeks.
Face-to-face discussions resumed in London over the weekend, after chief EU negotiator Michel Barnier left self-isolation following a colleague’s positive Covid-19 test last week.
The two sides are trying to strike an agreement to govern their trading relationship after the UK’s post-Brexit transition period ends on 31 December.
Speaking on the BBC’s Andrew Marr programme, Mr Raab said: “We’re down to really two basic issues, but I think in particular the issue around fisheries.
“I do think this is a very significant week, the last real major week, subject to any further postponement of the goalposts in terms of the timing.”
He added that a deal was subject to the EU accepting the “point of principle” that the UK would require “control” over its fishing grounds after the transition.
“If the EU understand that point of principle and we have some pragmatism, we can get there,” he said.