Barnier also warned that failure to resolve the Irish border question could still derail any deal.
More positive noises out of Brussels about reaching a Brexit trade agreement - the dominant driver of sterling - have been offset by growing unhappiness within Prime Minister Theresa May's own party and her rivals about the sort of Brexit agreement she wants to forge.
"A domestic political storm may well be about to hit London. The latest move to extend the transition period beyond December 2020 looks to have really destabilised the domestic political landscape," said MUFG analysts in a note.
"A break below $1.3000 in GBP/USD looks inevitable now, and of course this scenario reinforces EUR/USD downside risks as well."
Sterling rose to a day's high versus the dollar of $1.3038 after Barnier's comments, before extending to as high as $1.3047.
Official data showing Britain's government recorded a smaller budget deficit than expected in September also provided some support to the currency.
The pound was 0.2 percent higher against the euro to 87.785 pence.
"Ninety percent of the accord on the table has been agreed with Britain," Barnier told France Inter radio, adding that the Irish border issue remained a sticking point and could derail any agreement.
On Thursday, May and other EU leaders voiced renewed confidence that they could secure a Brexit deal, yet the two sides remain at odds over how to deal with their only land border, between the British province of Northern Ireland and Ireland.
May had also signalled that she would consider extending a so-called transition period "for a matter of months" after Britain leaves the EU at the end of March.
Britain's Foreign Minister Jeremy Hunt said on Friday it would be hard to resolve the issue of a backstop to the Irish border problem in Brexit talks without more detail on the future relationship with the EU after Brexit.
In a note to clients on Friday, RBC analysts said there had been no improvement "whatsoever" in British export performance despite sterling tumbling and remaining weak since the British voted to leave the EU in 2016.
"Unless domestic demand surprises to the upside, which seems unlikely, we still see downside export surprises as a key vulnerability for UK rates and GBP," they said.