Dominic Raab said this could be the last week of "substantive" negotiations as he urged Brussels to recognise the "point of principle" on Britain's control of its waters.
He told Sky's Sophy Ridge On Sunday: "I do think we're in a reasonable position - there's a deal to be done.
"If you look really at what the outstanding issues are, of course the level playing field, but it feels like there is progress towards greater respect for what the UK position was.
"On fishing there's a point of principle: as we leave the EU we're going to be an independent... coastal state and we've got to be able to control our waters."
Mr Raab said the UK recognised the impact on other countries, but said: "I think the answer is 'can the EU accept that point of principle which comes with us leaving the political club?".
The EU's chief negotiator Michel Barnier has been in London this weekend for talks with his UK counterpart Lord (David) Frost, but Downing Street said there remains a lot to do at a late hour.
Arriving at the talks on Sunday morning, Mr Barnier told reporters: "Work continues, even on a Sunday."
Progress is understood to have been made across many areas, yet significant gaps remain on the EU's access to UK fishing waters when the transition period ends on December 31.
Reports last week suggested that Mr Barnier recently said the EU could accept a 15-18% cut in its share of fishing rights in UK waters, but a Government source said: "These figures are risible, and the EU side know full well that we would never accept this.
"There seems to be a failure from the Commission to internalise the scale of change needed as we become an independent nation."
The Government has repeatedly said it is prepared to leave the transition period without a deal if the EU fails to move, and talks have been deadlocked for months over fishing rights and other issues.